中西 賢次

Last Update: 2019/09/20 15:31:03

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Name(Kanji/Kana/Abecedarium Latinum)
中西 賢次/ナカニシ ケンジ/Nakanishi, Kenji
Primary Affiliation(Org1/Job title)
Research Institute for Mathematical Sciences (RIMS)/Professor
Faculty
Org1 Job title
理学部
Contact Address
Type Address(Japanese) Address(English)
Office 606-8502 京都市左京区北白川追分町 京都大学 数理解析研究所 Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Kyoto 606-8502, JAPAN
Phone
Type Number
Office 075-753-7233
Academic Organizations You are Affiliated to in Japan
Organization name(Japanese) Organization name(English)
日本数学会 Mathematical Society of Japan
Academic Degree
Field(Japanese) Field(English) University(Japanese) University(English) Method
修士（数理科学） 東京大学
博士（数理科学） 東京大学
Work Experience
Period Organization(Japanese) Organization(English) Job title(Japanese) Job title(English)
1999/10/01-2001/07/31 神戸大学 Kobe University 助手 Research Associate
2001/08/01-2005/09/30 名古屋大学 Nagoya University 助教授 Associate Professor
2005/10/01-2015/03/31 京都大学 Kyoto University 准教授 Associate Professor
2015/04/01-2018/03/31 大阪大学 Osaka University 教授 Professor
Personal Profile
(Japanese)
偏微分方程式の研究をしている。大学院生の研究指導のほかに、理学部数学教室の学部生のセミナー指導などを行うこともある。
(English)
I am conduction research on partial differential equations. Besides research supervision for graduate students, I sometimes supervise seminars by undergraduate students of the department of mathematics.
ORCID ID
https://orcid.org/0000-0002-8988-1726
researchmap URL
https://researchmap.jp/7000008615
Research Topics
(Japanese)
偏微分方程式
(English)
Partial differential equations
Overview of the research
(Japanese)
私の研究分野は偏微分方程式の数学解析で，主な対象は非線形波動または非線形分散型と呼ばれる非線形偏微分方程式である。これらは，プラズマ・水面波・超流動・光ファイバーなど様々な物理的状況における，相互作用の強い波動の時空間発展を記述するもので，波の分散性と非線形相互作用の競合により色々な時間変化を現わすことができる。代表的なものは非線形 Schrödinger 方程式や KdV 方程式などが挙げられる。偏微分方程式の理論上もっとも基礎的な初期値問題の局所的可解性については，精密な線形および多重線形の関数評価式の整備によって，広範な方程式と関数空間を扱えるようになった。近年はそれに基づいて解の時間大域的様相の解析が進んでおり，典型的な解からそれらの複合的状況まで徐々に明らかにされつつある。私の近年の研究では一般解全体の様相を捉えることを目指し，特に，異なる典型的挙動の間の時間的遷移や，解空間の中での中間的状態の解析のため，技術開発と現象解明の両軸で研究を行っている。今後は力学系の観点に加えて確率的記述により全体像に近づくことを目論んでいる。下記論文リスト内の成果としては，散乱・ソリトン・爆発を含む解の時間大域挙動分類について，Schlag 達との９分類の結果をエネルギー臨界の Schrödinger 方程式に拡張した[4]。また，エネルギー臨界の波動方程式に対しては，基底状態ソリトン周りの中心(不)安定多様体とその近傍の大域挙動をエネルギー空間全体へ拡張した[10]。また，時間正方向の挙動について類似の３分類を与える不変多様体を，質量臨界 KdV 方程式に対して構成した[5]。更に，安定・不安定のソリトンを両方含む場合として，ポテンシャル付き非線形 Schrödinger 方程式の小質量球対称解について，第１励起エネルギーを少し超える範囲まで９分類した[2,3]。これは安定ソリトンとの無限時間相互作用で大域的分散成分が受ける影響を解析上克服した所がポイントである。一方，これらの大域解析を物理的に自然な低次非線形項に拡張すべく，一般の球対称 Fourier 積の方程式に対して球面平均の Strichatz 評価を導き，３次元非線形 Schrödinger 方程式の平面波解の球対称エネルギー摂動に対する漸近安定性を示した[1]。他には４次元の Zakharov 系に対して，エネルギー空間での可解性と散乱理論のため，２つの異なる空間での可解性と弱極限を組合わせた新しい論法を開発した[7]。非線形分散型以外に[9]では Trudinger-Moser 不等式を全平面の Schrödinger 型エネルギー制約下で調べ，有界性とコンパクト性に対する非線形項の必要十分条件を導出し，臨界増大度が有界領域の二乗指数関数から多項式で２次下がる事を示した。
(English)
My research subject is mathematical analysis of partial differential equations, mainly of those called nonlinear wave equations or nonlinear dispersive equations, which describe space-time evolution of waves with strong interactions, arising in several physical contexts, such as plasma, superfluid, and water waves. Depending on the competition between the dispersion and the nonlinear interactions, a single equation can typically produce many types of solutions, such as scattering, solitons, and blow-up. In recent years, the ultimate goal of my research has been to grasp the entire picture of all general solutions to some equations. I am particularly interested in understanding and describing possible transitions in time between various types of solutions, as well as in the intermediate or threshold solutions in the phase space.
Fields of research (key words)
Key words(Japanese) Key words(English)
偏微分方程式 Partial differential equations
Published Papers
Author Author(Japanese) Author(English) Title Title(Japanese) Title(English) Bibliography Bibliography(Japanese) Bibliography(English) Publication date Refereed paper Language Publishing type Disclose
Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi, Federica Sani Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi, Federica Sani Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities Journal of Functional Analysis Journal of Functional Analysis Journal of Functional Analysis 2019/08 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Takuto Yamamoto Kenji Nakanishi, Takuto Yamamoto Kenji Nakanishi, Takuto Yamamoto Randomized final-data problem for Systems of Nonlinear Schrödinger Equations and the Gross-Pitaevskii Equation Randomized final-data problem for Systems of Nonlinear Schrödinger Equations and the Gross-Pitaevskii Equation Randomized final-data problem for Systems of Nonlinear Schrödinger Equations and the Gross-Pitaevskii Equation Mathematical Research Letters, 26, 1, 253-279 Mathematical Research Letters, 26, 1, 253-279 Mathematical Research Letters, 26, 1, 253-279 2019/06 Refereed English Research paper(scientific journal) Disclose to all
Jason Murphy, Kenji Nakanishi Jason Murphy, Kenji Nakanishi Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations 2019/06 English Disclose to all
Slim Ibrahim, Hiroaki Kikuchi, Kenji Nakanishi, Juncheng Wei Slim Ibrahim, Hiroaki Kikuchi, Kenji Nakanishi, Juncheng Wei Non-uniqueness for an energy-critical heat equation on R2 Non-uniqueness for an energy-critical heat equation on R2 Non-uniqueness for an energy-critical heat equation on R2 2019/05 English Disclose to all
Zihua Guo, Ji Li, Kenji Nakanishi, Lixin Yan Zihua Guo, Ji Li, Kenji Nakanishi, Lixin Yan Zihua Guo, Ji Li, Kenji Nakanishi, Lixin Yan On the boundary Strichartz estimates for wave and Schrödinger equations On the boundary Strichartz estimates for wave and Schrödinger equations On the boundary Strichartz estimates for wave and Schrödinger equations J. Differential Equations, 265, 11, 5656-5675 J. Differential Equations, 265, 11, 5656-5675 J. Differential Equations, 265, 11, 5656-5675 2018/12 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Kenji Nakanishi Zihua Guo, Kenji Nakanishi The Zakharov system in 4D radial energy space below the ground state The Zakharov system in 4D radial energy space below the ground state The Zakharov system in 4D radial energy space below the ground state 2018/10 English Disclose to all
Zihua Guo, Zaher Hani, Kenji Nakanishi Zihua Guo, Zaher Hani, Kenji Nakanishi Zihua Guo, Zaher Hani, Kenji Nakanishi Scattering for the 3D Gross-Pitaevskii equation Scattering for the 3D Gross-Pitaevskii equation Scattering for the 3D Gross-Pitaevskii equation Communications in Mathematical Physics, 359, 1, 265-295 Communications in Mathematical Physics, 359, 1, 265-295 Communications in Mathematical Physics, 359, 1, 265-295 2018/04 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi 中西 賢次 Kenji Nakanishi Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential. Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential. Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potential. Journal of the Mathematical Society of Japan, 69, 4, 1353-1401 Journal of the Mathematical Society of Japan, 69, 4, 1353-1401 Journal of the Mathematical Society of Japan, 69, 4, 1353-1401 2017/10 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi 中西 賢次 Kenji Nakanishi Global dynamics above the first excited energy for the nonlinear Schrödinger equation with a potential. Global dynamics above the first excited energy for the nonlinear Schrödinger equation with a potential. Global dynamics above the first excited energy for the nonlinear Schrödinger equation with a potential. Communications in Mathematical Physics, 354, 1, 161-212 Communications in Mathematical Physics, 354, 1, 161-212 Communications in Mathematical Physics, 354, 1, 161-212 2017/05 Refereed English Research paper(scientific journal) Disclose to all
Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Correction to the article Scattering threshold for the focusing nonlinear Klein-Gordon equation Correction to the article Scattering threshold for the focusing nonlinear Klein-Gordon equation Correction to the article Scattering threshold for the focusing nonlinear Klein-Gordon equation Analysis & PDE, 9, 2, 503-514 Analysis & PDE, 9, 2, 503-514 Analysis & PDE, 9, 2, 503-514 2016/03 Refereed Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Tristan Roy 中西 賢次 Kenji Nakanishi, Tristan Roy Global dynamics above the ground state for the energy-critical Schrödinger equation with radial data. Global dynamics above the ground state for the energy-critical Schrödinger equation with radial data. Global dynamics above the ground state for the energy-critical Schrödinger equation with radial data. Communications on Pure and Applied Analysis, 15, 6, 2023-2058 Communications on Pure and Applied Analysis, 15, 6, 2023-2058 Communications on Pure and Applied Analysis, 15, 6, 2023-2058 2016 Refereed Japanese Research paper(scientific journal) Disclose to all
Yvan Martel, Frank Merle, Kenji Nakanishi, Pierre Raphael 中西 賢次 Yvan Martel, Frank Merle, Kenji Nakanishi, Pierre Raphael Codimension one threshold manifold for the critical gKdV equation. Codimension one threshold manifold for the critical gKdV equation. Codimension one threshold manifold for the critical gKdV equation. Communications in Mathematical Physics, 342, 3, 1075-1106 Communications in Mathematical Physics, 342, 3, 1075-1106 Communications in Mathematical Physics, 342, 3, 1075-1106 2015/11 Refereed English Research paper(scientific journal) Disclose to all
Chongsheng Cao, Slim Ibrahim, Kenji Nakanishi, Edriss S. Titi Chongsheng Cao, Slim Ibrahim, Kenji Nakanishi, Edriss S. Titi Chongsheng Cao, Slim Ibrahim, Kenji Nakanishi, Edriss S. Titi Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics Communications in Mathematical Physics, 337, 2, 473-482 Communications in Mathematical Physics, 337, 2, 473-482 Communications in Mathematical Physics, 337, 2, 473-482 2015/07 Refereed English Research paper(scientific journal) Disclose to all
Ioan Bejenaru, Zihua Guo, Sebastian Herr, Kenji Nakanishi Ioan Bejenaru, Zihua Guo, Sebastian Herr, Kenji Nakanishi Ioan Bejenaru, Zihua Guo, Sebastian Herr, Kenji Nakanishi Well-posedness and scattering for the Zakharov system in four dimensions Well-posedness and scattering for the Zakharov system in four dimensions Well-posedness and scattering for the Zakharov system in four dimensions Analysis & PDE 8-8 (2015), 2029-2055 Analysis & PDE 8-8 (2015), 2029-2055 Analysis & PDE 8-8 (2015), 2029-2055 2015/04/05 Research paper(scientific journal) Disclose to all
Dan-Andrei Geba, Kenji Nakanishi, Xiang Zhang Dan-Andrei Geba, Kenji Nakanishi, Xiang Zhang Dan-Andrei Geba, Kenji Nakanishi, Xiang Zhang Sharp global regularity for the 2+1-dimensional equivariant Faddeev model Sharp global regularity for the 2+1-dimensional equivariant Faddeev model Sharp global regularity for the 2+1-dimensional equivariant Faddeev model International Mathematics Research Notices, 2015, 22, 11549-11565 International Mathematics Research Notices, 2015, 22, 11549-11565 International Mathematics Research Notices, 2015, 22, 11549-11565 2015/02 Refereed English Research paper(scientific journal) Disclose to all
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Center-stable manifold of the ground state in the energy space for the critical wave equation Center-stable manifold of the ground state in the energy space for the critical wave equation Center-stable manifold of the ground state in the energy space for the critical wave equation Mathematische Annalen, 361, 1-2, 1-50 Mathematische Annalen, 361, 1-2, 1-50 Mathematische Annalen, 361, 1-2, 1-50 2015/02 Refereed English Research paper(scientific journal) Disclose to all
Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Trudinger-Moser inequality on the whole plane with the exact growth condition Trudinger-Moser inequality on the whole plane with the exact growth condition Trudinger-Moser inequality on the whole plane with the exact growth condition Journal of the European Mathematical Society, 17, 4, 819-835 Journal of the European Mathematical Society, 17, 4, 819-835 Journal of the European Mathematical Society, 17, 4, 819-835 2015 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Sanghyuk Lee, Kenji Nakanishi, Chengbo Wang Zihua Guo, Sanghyuk Lee, Kenji Nakanishi, Chengbo Wang Zihua Guo, Sanghyuk Lee, Kenji Nakanishi, Chengbo Wang Generalized Strichartz estimates and scattering for 3D Zakharov system Generalized Strichartz estimates and scattering for 3D Zakharov system Generalized Strichartz estimates and scattering for 3D Zakharov system Communications in Mathematical Physics, 331, 1, 239-259 Communications in Mathematical Physics, 331, 1, 239-259 Communications in Mathematical Physics, 331, 1, 239-259 2014/10 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case Communications in Partial Differential Equations, 39, 6, 1158-1184 Communications in Partial Differential Equations, 39, 6, 1158-1184 Communications in Partial Differential Equations, 39, 6, 1158-1184 2014/05 Refereed English Research paper(scientific journal) Disclose to all
Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation Trans. Amer. Math. Soc., 366, 5653-5669 Trans. Amer. Math. Soc., 366, 5653-5669 Trans. Amer. Math. Soc., 366, 5653-5669 2014/05 Refereed English Research paper(scientific journal) Disclose to all
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Threshold phenomenon for the quintic wave equation in three dimensions Threshold phenomenon for the quintic wave equation in three dimensions Threshold phenomenon for the quintic wave equation in three dimensions Communications in Mathematical Physics, 327, 1, 309-332 Communications in Mathematical Physics, 327, 1, 309-332 Communications in Mathematical Physics, 327, 1, 309-332 2014/04 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetry Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetry Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetry Mathematical Research Letters, 21, 4, 733-755 Mathematical Research Letters, 21, 4, 733-755 Mathematical Research Letters, 21, 4, 733-755 2014 Refereed English Research paper(scientific journal) Disclose to all
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Global dynamics away from the ground state for the energy-critical nonlinear wave equation Global dynamics away from the ground state for the energy-critical nonlinear wave equation Global dynamics away from the ground state for the energy-critical nonlinear wave equation American Journal of Mathematics, 135, 4, 935-965 American Journal of Mathematics, 135, 4, 935-965 American Journal of Mathematics, 135, 4, 935-965 2013/08 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Zihua Guo, Kenji Nakanishi, Shuxia Wang Global dynamics below the ground state energy for the Zakharov system in the 3D radial case Global dynamics below the ground state energy for the Zakharov system in the 3D radial case Global dynamics below the ground state energy for the Zakharov system in the 3D radial case Advances in Mathematics, 238, 1, 412-441 Advances in Mathematics, 238, 1, 412-441 Advances in Mathematics, 238, 1, 412-441 2013/05 Refereed English Research paper(scientific journal) Disclose to all
Zihua Guo, Kenji Nakanishi Zihua Guo, Kenji Nakanishi Zihua Guo, Kenji Nakanishi Small energy scattering for the Zakharov system with radial symmetry Small energy scattering for the Zakharov system with radial symmetry Small energy scattering for the Zakharov system with radial symmetry International Mathematics Research Notices, 2014, 9, 2327-2342 International Mathematics Research Notices, 2014, 9, 2327-2342 International Mathematics Research Notices, 2014, 9, 2327-2342 2013/01 Refereed English Research paper(scientific journal) Disclose to all
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Global dynamics of the nonradial energy-critical wave equation above the ground state energy Global dynamics of the nonradial energy-critical wave equation above the ground state energy Global dynamics of the nonradial energy-critical wave equation above the ground state energy Discrete and Continuous Dynamical Systems, 33, 6, 2423-2450 Discrete and Continuous Dynamical Systems, 33, 6, 2423-2450 Discrete and Continuous Dynamical Systems, 33, 6, 2423-2450 2013 Refereed English Research paper(scientific journal) Disclose to all
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag Global dynamics above the ground state energy for the one-dimensional NLKG equation Global dynamics above the ground state energy for the one-dimensional NLKG equation Global dynamics above the ground state energy for the one-dimensional NLKG equation Mathematische Zeitschrift, 272, 1-2, 297-316 Mathematische Zeitschrift, 272, 1-2, 297-316 Mathematische Zeitschrift, 272, 1-2, 297-316 2012/10 Refereed English Research paper(scientific journal) Disclose to all
Dan-Andrei Geba, Kenji Nakanishi, Sarada G. Rajeev Dan-Andrei Geba, Kenji Nakanishi, Sarada G. Rajeev Dan-Andrei Geba, Kenji Nakanishi, Sarada G. Rajeev Global well-posedness and scattering for Skyrme wave maps Global well-posedness and scattering for Skyrme wave maps Global well-posedness and scattering for Skyrme wave maps Communications on Pure & Applied Analysis, 11, 5, 1923-1933 Communications on Pure & Applied Analysis, 11, 5, 1923-1933 Communications on Pure & Applied Analysis, 11, 5, 1923-1933 2012/09 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Tuoc Van Phan, Tai-Peng Tsai Kenji Nakanishi, Tuoc Van Phan, Tai-Peng Tsai Kenji Nakanishi, Tuoc Van Phan, Tai-Peng Tsai Small solutions of nonlinear Schrödinger equations near first excited states Small solutions of nonlinear Schrödinger equations near first excited states Small solutions of nonlinear Schrödinger equations near first excited states Journal of Functional Analysis, 263, 3, 703-781 Journal of Functional Analysis, 263, 3, 703-781 Journal of Functional Analysis, 263, 3, 703-781 2012/08 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Global dynamics above the ground state energy for the cubic NLS equation in 3D Global dynamics above the ground state energy for the cubic NLS equation in 3D Global dynamics above the ground state energy for the cubic NLS equation in 3D Calculus of Variations and Partial Differential Equations, 44, 1-2, 1-45 Calculus of Variations and Partial Differential Equations, 44, 1-2, 1-45 Calculus of Variations and Partial Differential Equations, 44, 1-2, 1-45 2012/05 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equation SIAM Journal on Mathematical Analysis, 44, 2, 1175-1210 SIAM Journal on Mathematical Analysis, 44, 2, 1175-1210 SIAM Journal on Mathematical Analysis, 44, 2, 1175-1210 2012/04 Refereed English Research paper(scientific journal) Disclose to all
Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Kenji Nakanishi, Wilhelm Schlag Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation Journal of Differential Equations, 250, 5, 2299-2333 Journal of Differential Equations, 250, 5, 2299-2333 Journal of Differential Equations, 250, 5, 2299-2333 2011/03/01 Refereed English Research paper(scientific journal) Disclose to all
Lassaad Aloui, Slim Ibrahim, Kenji Nakanishi Lassaad Aloui, Slim Ibrahim, Kenji Nakanishi Lassaad Aloui, Slim Ibrahim, Kenji Nakanishi Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth Communications in Partial Differential Equations, 36, 5, 797-818 Communications in Partial Differential Equations, 36, 5, 797-818 Communications in Partial Differential Equations, 36, 5, 797-818 2011/01 Refereed English Research paper(scientific journal) Disclose to all
Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi Scattering threshold for the focusing nonlinear Klein-Gordon equation Scattering threshold for the focusing nonlinear Klein-Gordon equation Scattering threshold for the focusing nonlinear Klein-Gordon equation Analysis & PDE, 4, 3, 405-460 Analysis & PDE, 4, 3, 405-460 Analysis & PDE, 4, 3, 405-460 2011 Refereed English Research paper(scientific journal) Disclose to all
Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi, Kenji Nakanishi Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi, Kenji Nakanishi Scattering for the two-dimensional energy-critical wave equation Scattering for the two-dimensional energy-critical wave equation Scattering for the two-dimensional energy-critical wave equation Duke Math. J., 150, 2, 287-329 Duke Math. J., 150, 2, 287-329 Duke Math. J., 150, 2, 287-329 2009/11/01 Refereed English Research paper(scientific journal) Disclose to all
Shu-Ming Chang, Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Shu-Ming Chang, Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Shu-Ming Chang, Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Spectra of Linearized Operators for NLS Solitary Waves Spectra of Linearized Operators for NLS Solitary Waves Spectra of Linearized Operators for NLS Solitary Waves SIAM Journal on Mathematical Analysis, 39, 4, 1070-1111 SIAM Journal on Mathematical Analysis, 39, 4, 1070-1111 SIAM Journal on Mathematical Analysis, 39, 4, 1070-1111 2006/11 Refereed English Research paper(scientific journal) Disclose to all
Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves International Mathematics Research Notices, 66, 3559-3584 International Mathematics Research Notices, 66, 3559-3584 International Mathematics Research Notices, 66, 3559-3584 2004/01 Refereed English Research paper(scientific journal) Disclose to all

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Title language:
Conference Activities & Talks
Title Title(Japanese) Title(English) Conference Conference(Japanese) Conference(English) Promotor Promotor(Japanese) Promotor(English) Date Language Assortment Disclose
調和写像のSchrodinger及び熱流における漸近安定性と永久振動集約 調和写像のSchrodinger及び熱流における漸近安定性と永久振動集約 京大・理 京大・理 2006 Japanese Disclose to all
Title language:
Books etc
Author Author(Japanese) Author(English) Title Title(Japanese) Title(English) Publisher Publisher(Japanese) Publisher(English) Publication date Language Type Disclose
Kenji Nakanishi & Wilhelm Schlag Kenji Nakanishi & Wilhelm Schlag Invariant Manifolds and Dispersive Hamiltonian Evolution Equations Invariant Manifolds and Dispersive Hamiltonian Evolution Equations European Mathematical Society European Mathematical Society 2011 English Disclose to all
Title language:
External funds: competitive funds and Grants-in-Aid for Scientific Research (Kakenhi)
Type Position Title(Japanese) Title(English) Period
若手研究（Ｂ） Representative 非線形波動の大域的分散性 2006/04/01-2009/03/31
若手研究（B） Representative 非線形波動の分散と共鳴の大域解析 2009/04/01-2013/03/31
特別研究員奨励費 Representative 非線形波動方程式の超臨界大域解析 2011-2013
基盤研究（Ｃ） Representative 非線形分散型方程式の大域ダイナミクス 2013/04/01-2017/03/31
基盤研究(B) Representative 非線形波動方程式の大域ダイナミクス 2017/04/01-2022/03/31
基盤研究(B) Representative 非線形波動方程式の大域ダイナミクス （平成30年度分） 2018/04/01-2019/03/31
Teaching subject(s)
Name(Japanese) Name(English) Term Department Period
微分積分学Ａ[理学部] Calculus A 前期 全学共通科目 2011/04-2012/03
微分積分学Ｂ[理学部] Calculus B 後期 全学共通科目 2011/04-2012/03
数学講究 通年 理学部 2011/04-2012/03
解析学演義Ｉ 前期 理学部 2011/04-2012/03
微分積分学Ａ Calculus A 前期 全学共通科目 2012/04-2013/03
線形代数学Ａ Linear Algebra A 前期 全学共通科目 2012/04-2013/03
線形代数学Ｂ Linear Algebra B 後期 全学共通科目 2012/04-2013/03
解析学特論III Advanced Analysis III 後期 理学部 2012/04-2013/03
解析学Ｉ Analysis I 前期 理学部 2013/04-2014/03
微分積分学Ａ Calculus A 前期 全学共通科目 2013/04-2014/03
微分積分学Ｂ Calculus B 後期 全学共通科目 2013/04-2014/03
解析学演義II Exercises in Analysis II 後期 理学部 2014/04-2015/03
数学講究 Mathematics seminary 通年 理学部 2014/04-2015/03
微分方程式論数学先端研究Ａ Seminar on Differential Equations A 前期 理学研究科 2014/04-2015/03
微分方程式論数学先端研究Ｂ Seminar on Differential Equations B 後期 理学研究科 2014/04-2015/03
微分方程式論数学先端研究Ｃ Seminar on Differential Equations C 前期 理学研究科 2014/04-2015/03
微分方程式論数学先端研究Ｄ Seminar on Differential Equations D 後期 理学研究科 2014/04-2015/03
微分積分学Ａ Calculus A 前期 全学共通科目 2014/04-2015/03
微分積分学Ｂ Calculus B 後期 全学共通科目 2014/04-2015/03
偏微分方程式セミナー研究ａ Seminar on Partial Differential Equations a 前期 理学研究科 2018/04-2019/03
偏微分方程式セミナー研究ｂ Seminar on Partial Differential Equations b 後期 理学研究科 2018/04-2019/03
偏微分方程式セミナー研究ｃ Seminar on Partial Differential Equations c 前期 理学研究科 2018/04-2019/03
偏微分方程式セミナー研究ｄ Seminar on Partial Differential Equations d 後期 理学研究科 2018/04-2019/03
数学講究 Mathematics seminary 通年 理学部 2018/04-2019/03
偏微分方程式セミナー研究ａ Seminar on Partial Differential Equations a 前期 理学研究科 2019/04-2020/03
偏微分方程式セミナー研究ｂ Seminar on Partial Differential Equations b 後期 理学研究科 2019/04-2020/03
偏微分方程式セミナー研究ｃ Seminar on Partial Differential Equations c 前期 理学研究科 2019/04-2020/03
偏微分方程式セミナー研究ｄ Seminar on Partial Differential Equations d 後期 理学研究科 2019/04-2020/03

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Academic organizations (editor, editing team)
Organization name(Japanese) Organization name(English) Journal name(Japanese) Journal name(English) Title Period
日本数学会 Mathematical Society of Japan Advanced Studies in Pure Mathematics Editor 2017/07/01-
日本数学会 Mathematical Society of Japan Journal of the Mathematical Society of Japan Editor 2018/07/01-2024/06/30
Mathematical Society of the Republic of China Taiwanese Journal of Mathematics Editor 2019/04/01-

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