Updated on 2024/02/15
博士（数理科学） ( 東京大学 )
修士（数理科学） ( 東京大学 )
Tohoku University Graduate School, Division of Natural Science others others
The University of Tokyo Graduate School, Division of Mathematical Sciences doctor course completed
The University of Tokyo Graduate School, Division of Mathematical Sciences master course completed
The University of Tokyo graduated
2018.4 -
中央大学理工学部教授
2007.4 - 2018.3
名古屋大学大学院多元数理科学研究科・准教授
2015.4 - 2016.3
京都大学大学院理学研究科非常勤講師
2015.8
清華大学（中国）集中講義講師
2011.5 - 2012.3
トロント大学客員研究員(日本学術振興会特定国派遣研究者)
2005.4 - 2007.3
名古屋大学大学院多元数理科学研究科・助教授
2005.3
マックスプランク数学研究所（ライプチヒ）ポストドクター
2004.9 - 2005.3
スイス連邦工科大学ポストドクター
2003.9 - 2004.9
フランス高等科学研究所ポストドクター
2003.4 - 2003.9
東北学院大学工学部環境土木工学科非常勤講師
日本数学会
partial differential equations
Natural Science / Basic analysis / 解析学基礎
Well-posedness and parabolic smoothing effect for higher order Schrodinger type equations with constant coefficients Reviewed
Tomoyuki TANAKA, Kotaro TSUGAWA
Osaka J. Math. 59 465 - 480 2022.2
SCATTERING AND WELL-POSEDNESS FOR THE ZAKHAROV SYSTEM AT A CRITICAL SPACE IN FOUR AND MORE SPATIAL DIMENSIONS Reviewed
Isao Kato, Kotaro Tsugawa
DIFFERENTIAL AND INTEGRAL EQUATIONS 30 ( 9-10 ) 763 - 794 2017.9
Local well-posedness and parabolic smoothing effect of fifth order dispersive equations on the torus Reviewed
K. Tsugawa
RIMS Kokyuroku Bessatsu B60 177 - 193 2016.12
LOCAL WELL-POSEDNESS OF THE KDV EQUATION WITH QUASI-PERIODIC INITIAL DATA Reviewed
Kotaro Tsugawa
SIAM JOURNAL ON MATHEMATICAL ANALYSIS 44 ( 5 ) 3412 - 3428 2012
LOCAL WELL-POSEDNESS FOR QUADRATIC NONLINEAR SCHRODINGER EQUATIONS AND THE "GOOD" BOUSSINESQ EQUATION Reviewed
Nobu Kishimoto, Kotaro Tsugawa
DIFFERENTIAL AND INTEGRAL EQUATIONS 23 ( 5-6 ) 463 - 493 2010.5
Well-posedness for nonlinear Dirac equations in one dimension Reviewed
Shuji Machihara, Kenji Nakanishi, Kotaro Tsugawa
Kyoto Journal of Mathematics 50 ( 2 ) 403 - 451 2010
Well-posedness and weak rotation limit for the Ostrovsky equation Reviewed
Kotaro Tsugawa
JOURNAL OF DIFFERENTIAL EQUATIONS 247 ( 12 ) 3163 - 3180 2009.12
Well-posedness for quadratic nonlinear Schrodinger equations Reviewed
K. Tsugawa
RIMS Kokyuroku Bessatsu B14 163 - 173 2009.11
Global well-posedness for the KdV equations on the real line with low regularity forcing terms Reviewed
Kotaro Tsugawa
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 8 ( 5 ) 681 - 713 2006.10
Existence of the global attractor for weakly damped, forced KDV equation on Sobolev spaces of negative index Reviewed
K Tsugawa
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 3 ( 2 ) 301 - 318 2004.6
I-method with application to damped forced KdV equation
K. Tsugawa
Surikaisekikenkyusho Kokyuroku 1355 48 - 67 2004.1
K. Tsugawa
Surikaisekikenkyusho Kokyuroku 1331 84 - 92 2003.7
Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions Reviewed
H Kubo, K Tsugawa
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 9 ( 2 ) 471 - 482 2003.3
K. Tsugawa
Surikaisekikenkyusho Kokyuroku 1235 61 - 90 2001.10
Well-posedness in the energy space for the Cauchy problem of the coupled system of complex scalar field and Maxwell equations Reviewed
K. Tsugawa
Funkcialaj Ekvacioj 43 127 - 161 2000.4
K. Tsugawa
Surikaisekikenkyusho Kokyuroku 1135 85 - 90 2000.4
Well-posedness and parabolic smoothing effect for higher order Schrodinger type equations with constant coefficients Invited
Kotaro TSUGAWA
神楽坂解析セミナー 2020.11
Well-posedness and parabolic smoothing effect for higher order linear Schrodinger type equations on the torus Invited International conference
Kotaro TSUGAWA
The 37th Kyushu Symposium on Partial Differential Equations 2020.1
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
東北大学応用数学セミナー ( 東北大学理学研究科 ) 2018.7
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
応用解析研究会 ( 早稲田大学 ) 2018.5
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
調和解析中大セミナー ( 中央大学理工学部 ) 2018.4
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
中大偏微分方程式セミナー ( 中央大学理工学部 ) 2018.4
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
津田塾大学PDE研究会 2018.2
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
第2回 PDE Workshop in Miyazaki, 宮崎大学 2018.1
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
第7回弘前非線形方程式研究会, 弘前大学 2017.12
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
京都大学NLPDEセミナー 2017.6
Ill-posedness of derivative nonlinear Schrodinger equations on the torus
名古屋微分方程式セミナー 2017.5
Local well-posedness of derivative nonlinear Schrodinger equations on the torus
Critical Exponents and Nonlinear Evolution Equation 2017.2
Local well-posedness and parabolic smoothing effect of semilinear dispersive equations
第３回 神楽坂非線形波動研究会 2016.12
Parabolic smoothing effect and local well-posedness of semilinear fifth order dispersive equations on the torus
Taiwan-Japan Workshop on Dispersion, Navier Stokes, Kinetic, and Inverse Problems 2016.12
Local well-posedness and parabolic smoothing effect of semilinear fifth order dispersive equations on the torus
Harmonic Analysis, Geometric Analysis and PDE Workshop 2016.3
Parabolic smoothing effect and local well-posedness of fifth order|rn|dispersive equations on the torus
松山解析セミナー2016, 愛媛大学 2016.2
Parabolic smoothing effect and local well-posedness of fifth order|rn|dispersive equations on the torus
波動セミナー(ワークショップ), 北海道大学 2016.2
5階の分散型方程式の局所適切性と放物型平滑化効果
京都大学数理解析研究所談話会 2015.11
Refined energy estimate and local well-posedness|rn| of fifth order dispersive equations on the torus
熊本大学応用解析セミナー 2015.8
Refined energy estimate and local well-posedness|rn| of fifth order dispersive equations on the torus
RIMS研究集会「調和解析と非線形偏微分方程式」 2015.7
Refined energy estimate and local well-posedness|rn| of fifth order dispersive equations on the torus
Nonlinear Evolution Equations and Related Topics 2015.3
Refined energy estimate and local well-posedness|rn| of fifth order dispersive equations on the torus
九州関数方程式セミナー 2014.12
Refined energy estimate and local well-posedness|rn|of fifth order dispersive equations on the torus
The 12th Linear and Nonlinear Waves 2014.11
Refined energy estimate and local well-posedness|rn|of fifth order dispersive equations on the torus
第1回神楽坂非線形波動研究会 2014.10
5階の非線形分散型方程式の局所適切性
日本数学会秋季総合分科会特別講演 2014.9
A cancellation property and the well-posedness of fifth order KdV type equations on the torus
Critical Exponents and Nonlinear Evolution Equation 2014.2
Well-posedness of the KdV equation with almost periodic initial data
第9回非線型の諸問題, 高知大学 2013.9
On the normal form reduction
2013 Participating School in Analysis of PDE Global theory of nonlinear dispersive equations 2013.8
Unconditional well-posedness of the fifth order modified KdV equation with periodic boundary condition
Workshop on Nonlinear Dispersive PDEs 2012.8
Well-posedness of the KdV equation with almost periodic initial data
京都大学NLPDE セミナー 2012.5
Global well posedness of a stochastic KdV equation
RIMS短期共同研究「非線形分散型方程式における最近の進展」 2012.5
Well-posedness of the KdV equation with almost periodic initial data
名古屋微分方程式セミナー 2012.4
Well-posedness of the KdV equation with almost periodic initial data
非線形偏微分方程式研究会 2012.3
Local well-posedness of the KdV equation with almost periodic initial data, Analysis seminar
Analysis seminar,Princeton University 2011.11
Local well-posedness of the KdV equation with almost periodic initial data, Analysis seminar
Math Seminar, University of Toronto 2011.10
Local well-posedness of the KdV equation with almost periodic initial data
the 19th Workshop on Differential Equations and its Applications, National Cheng Kung University 2011.1
Local well-posedness for quadratic nonlinear Schrodinger equations
Analysis seminar, Courant Institute 2010.3
Local well-posedness for quadratic nonlinear Schrodinger equations, PDE seminar
PDE seminar, Brown University 2010.3
Local well-posedness for the Zakharov system in one space dimension
NLPDE seminar 2010.1
Well-posedness for the Zakharov system and Schrodinger equations with a potential term
研究集会「微分方程式の総合的研究」 2009.12
Local well-posedness for the Zakharov system in one space dimension
mini workshop 2009.11
Remark on the local well-posedness of the 1D Zakharov system
RIMS 短期共同研究「非線形双曲型および分散型方程式の解の挙動について」 2009.5
Remark on the time local well-posedness of the 1D Zakharov system
臨時セミナー, パリ南大学 2009.3
Well-posedness and weak rotation limit for the Ostrovsky quation
Workshop on Partial Differential Equations 2008.7
Well-posedness and weak rotation limit for the Ostrovsky quation
7th AIMS International conference on Dynamical Systems, Differential Equations and Applications 2008.5
A bilinear estimate related to the Dirac-Klein-Gordon equations and the wave maps in one space dimension
Linear and Nonlinear Waves, No.5 2007.11
Low regularity well-posedness of systems of transport equations
NLPDE seminar 2007.10
Well-posedness and weak rotation limit for the Ostrovsky quation
第４回浜松偏微分方程式研究集会 2006.12
Well-posedness and weak rotation limit for the Ostrovsky quation
Sapporo Guest House Symposium on Mathematics 22"Nonlinear wave equations" 2006.11
Well-posedness and weak rotation limit for the Ostrovsky quation
日本数学会2006年度秋季総合分科会 2006.9
A remark on Koch-Tzvetkov type estimates
RIMS研究集会「非線形分散型・波動方程式における解の漸近挙動」 2006.5
滑らかさの低い外力を持つKdV方程式の可解性
応用数学セミナー, 東北大学 2005.11
Global well-posedness for the forced KdV equations
日本数学会2005年度秋季総合分科会 2005.9
Global well-posedness for the forced KdV equations
応用解析セミナー, 熊本大学 2005.9
フーリエ制限法のKdV方程式への応用
第27回発展方程式若手セミナー 2005.8
Global well-posedness of the KdV equations with low regularity forcing terms
The 14th MSJ-IRI``Asymptotic Analysis and Singularity'' 2005.7
滑らかさの低い外力項を持つKdV方程式の適切性
解析ゼミ, 埼玉大学 2005.6
滑らかさの低い外力項を持つKdV方程式の可解性について
微分方程式セミナー, 大坂大学 2005.6
Time global behavior of the solutions of the KdV equations with low regularity forcing terms
Seminaire d'analyse appliquee A3, Universite de Picardie-Jules Verne 2004.6
Global well-posedness for the KdV equations with low regularity forcing terms
Seminaire d'equations aux derivees partielles non lineaires, Universite paris-sud 2004.6
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
非線形偏微分方程式阪大セミナー，大阪大学 2003.7
I-method with application to damped forced KdV equation
RIMS短期共同研究集会「非線形波動および分散型方程式に関する研究」 2003.5
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
Fourth Northeastern Symposium on Mathematical Analysis 2003.2
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
Nonlinear wave equations and related fields 2003.2
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
解析セミナー，神戸大学 2002.11
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
研究集会「非線形波動及び分散型方程式に関する最近の発展について」，大阪大学 2002.10
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
広島数理解析セミナー，広島大学 2002.10
Global existence of solutions to systems of wave equations with different propagation speeds in one space dimensions
日本数学会秋季総合分科会，島根大学 2002.9
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
日本数学会秋季総合分科会，島根大学 2002.9
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
第27回偏微分方程式論札幌シンポジウム，北海道大学 2002.8
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
Nonlinear wave equation and related topics 2002.7
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
非線形数理集中セミナー, 東京工業大学 2002.7
Existence of the global attractor for weakly damped, forced KdV equations on Sobolev space of negative index
第２４回神楽坂解析セミナー, 東京理科大学 2002.6
伝播速度の違う波動方程式がカップルしたシステム---特にstrongly coupled caseについて---
研究集会「非線形双曲型方程式系の解の挙動に関する研究」，京都大学数理解析研究所 2002.5
Time local well-posedness for the coupled system of wave equations with different propagation speeds
研究集会「非線型波動方程式系の解の構造」，北海道大学 2001.12
Time local well-posedness of the coupled system of nonlinear wave equations with different propagation speeds
調和解析学と非線形偏微分方程式研究集会, 京都大学数理解析研究所 2001.7
Time local well-posedness of the coupled system of nonlinear wave equations with different speeds
応用数学セミナー, 東北大学 2001.6
Time local well-posedness of the coupled system of nonlinear wave equations with different speeds
九大関数方程式セミナー 2001.5
Time local well-posedness for the coupled system of nonlinear wave equations with different propagation speeds
日本数学会2001年度年会 2001.3
Self-similar solutions of the coupled system of wave equations with different propagation speeds
日本数学会2001年度年会 2001.3
Self-similar solutions of the coupled system of wave equations with different propagation speeds
Workshop on Asymptotic Behavior of Solutions to Partial Differential Equations 2001.1
伝播速度の違う波動方程式のカップルしたシステムのtime local well-posedness について
解析学火曜セミナー，東京大学 2000.12
On the coupled system of nonlinear wave equations with different propagation speeds in spatial dimensions 1 and 2
日本数学会2000年度年会 2000.3
Local well-posedness for systems of wave equations with different propagation speeds
Sapporo Guest House Minisymposium 5 First Northeastern Symposium on Mathematical Analysis 2000.2
On the coupled system of nonlinear wave equations with different propagation speeds in two space dimension
Sapporo Guest House Minisymposium 3 Nonlinear Wave Equations 1999.11
On the coupled system of nonlinear wave equations with different propagation speeds in two space dimension
非線型発展方程式とその応用研究集会 1999.10
伝播速度の違う波動方程式のカップルしたシステムの時間局所適切性について
微分方程式セミナー，東北大学 1999.6
Well-posedness in the Energy space for the Cauchy problem of coupled system of complex scalar field and Maxwell equations
第2回箱根非線型発展方程式セミナー 1999.1
Well-posedness in the Energy space for the Cauchy problem of coupled system of complex scalar field and Maxwell equations
第20回発展方程式若手セミナー 1998.8
Well-posedness in the Energy space for the Cauchy problem of coupled system of complex scalar field and Maxwell equations
静岡大学・解析セミナー 1997.11
Well-posedness in the Energy space for the Cauchy problem of coupled system of complex scalar field and Maxwell equations
非線型双曲型, 分散型偏微分方程式の解の構造研究集会 1997.10
The Cauchy Problem for coupled Maxwell equation and scalar field
東京大学, 応用解析セミナーサマースクール 1997.9
The Cauchy Problem for coupled Maxwell equation and scalar field
日本数学会1997年度秋季総合分科会 1997.9
非線形分散型方程式の代数的構造と初期値問題の適切性
Grant number：17K05316 2017.4 - 2023.3
日本学術振興会 科学研究費助成事業 基盤研究(C)
津川 光太郎
Grant amount： \4550000 （ Direct Cost: \3500000 、 Indirect Cost： \1050000 ）
発展方程式の初期値問題において最も基本的な問題は適切性（解の存在、一意性、初期値に対する連続依存性）である。非線形分散型方程式の研究においては、これまで非線形項の特異性がそれほど強くない場合に対して多くの研究がなされてきた。しかし、非線形項に微分が含まれていて強い特異性を持つ場合は評価が難しく、今後の研究が期待されている。申請者の昨年度の研究では高階定数係数の線形シュレディンガー型方程式について研究を行い、初期値問題の適切性の結果が持つ特徴に基づいて方程式を分散型と放物型と楕円型に分類することに成功した。これを変数係数に拡張しさらには非線形方程式へと発展させていく予定であるが、今年度はそのための準備としてより単純な方程式である高階変数係数KdV型方程式について研究を行った。エネルギー法に基づいた手法で変数係数の方程式を本質的に定数係数の場合に帰着することに成功し、これを適切性の結果が持つ特徴により分類を行った。ここで得られた結果では、分類のための条件が帰納的に定義される複雑な結果した得られておらず、分類として具体的にどのような方程式を含んでいるかを計算により確かめることが難しい。また、将来、高階のシュレディンガー型方程式や非線形方程式へと研究をさたに発展させるためには、この段階においてより単純化された結果を得ることが出来ると便利である。現在はそのためにこらまでに得られた結果を改良中である。
An investigation of symmetries in the geometric structure and existence of global solutions to nonlinear dispersive wave equations
Grant number：25287022 2013.4 - 2018.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Takaoka Hideo, KUBO Hideo, NAKANISHI Kenji, TSUGAWA Kotaro
Grant amount： \16250000 （ Direct Cost: \12500000 、 Indirect Cost： \3750000 ）
In this study, I have developed the local and global well-posedness for the initial value problem related to the nonlinear Schrodinger equations in which dispersion effect and nonlinear interaction effect are incorporating. Using the Fourier analysis, I separated the solution into two parts; non-resonant and resonant oscillation parts, which have different in nature and distinguish nonuniformity part of solutions. For the nonlinear Schrodinger equations both with derivative in nonlinearities and on a sphere domain, I improved the local well-posedness for large function spaces. Moreover, I showed that there exists exchange of energy between Fourier modes. In the research process, I observed the estimation of energy exchange between different Fourier modes, due to the contribution in the nonlinear interaction.
Cauchy problem of nonlinear dispersive equations
Grant number：25400158 2013.4 - 2017.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) Nagoya University
Tsugawa Kotaro
Grant amount： \4940000 （ Direct Cost: \3800000 、 Indirect Cost： \1140000 ）
First, we proved the global well-posedness and asymptotic behavior of the Cauchy problem of Zakharov system in higher dimensions. We used the theory of Up, Vp space to prove it. The main difficulty comes from the difference of the properties of the linear equations. To overcome it, we used the intersection space of V2 space and Lebesgue space related to the end-point Strichartz estimate. Second, we categolized the fifth order KdV type equations. By using the normal form reduction, energy method and Bona-Smith approximation, we proved that the local well-posedness and parabolic smoothing effect.
geometric structure of nonlinearity and singularity of solutions for wave equations
Grant number：22740088 2010.4 - 2014.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B) Nagoya University
KOTARO Tsugawa
Grant amount： \3250000 （ Direct Cost: \2500000 、 Indirect Cost： \750000 ）
We studied the local and global well-posedness of the Cauchy problem for nonlinear dipersive equations and hyperbolic equations by the harmonic analysis. We improved the known results for a quadratic nonlinear Schrodinger equation and obtained the well-posedness result for low regularity data. The result is also applied to good Boussinesq equation. We showed the local well-posedness for nonlinear Dirac equation and Dirac-Klein-Gordon equation by using the property of null form. We also studied the Cauchy problem for the KdV equations with quasi periodic data.
Analysis of properties of solutions to dispersive equations via canonical transforms and comparison principle
Grant number：20340029 2008 - 2012
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) Nagoya University
SUGIMOTO Mitsuru, TSUGAWA Kotaro, KATO Jun, HISHIDA Toshiaki, MIYAKE Masatake, TACHIZAWA Kazuya, TOMITA Naohito
Grant amount： \18590000 （ Direct Cost: \14300000 、 Indirect Cost： \4290000 ）
By developing a global boundedness theory of Fourier integral operators, we established a method to deduce estimates for solutions to partial differential equations from those for their normal forms, and furthermore, prepared a new method to make a comparison of estimates for solutions from the comparison of symbols of two partial differential equations, so that we approached to nonlinear problems.
Solvability and properties of solutions of the Cauchy problem of equations related to the KdV equation
Grant number：18740068 2006 - 2008
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B) Nagoya University
TSUGAWA Tsugawa
Grant amount： \3800000 （ Direct Cost: \3500000 、 Indirect Cost： \300000 ）
Geometric approach to fluid mechanics
Grant number：18340025 2006 - 2008
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B) Nagoya University
KIMURA Yosifumi, KANAI Masahiko, NAGAO Taro, TSUGAWA Kotaro, MITSUMATSU Yoshihiko
Grant amount： \15390000 （ Direct Cost: \12900000 、 Indirect Cost： \2490000 ）
