On well-posedness of the Cauchy problem to Schrodinger maps in the energy space

• Project/Area Number: 20740073
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: KATO Jun 名古屋大学, 多元数理科学研究科, 准教授 (00432237)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 関数方程式 / 調和写像分散流 / シュレディンガー写像 / ストリッカーツ評価 / 非線型偏微分方程式論 / シュレディンガー方程式 / 関数方程式論 / 実関数論 / 数理物理 / 磁性

Research Abstract

We consider the well-posedness of the Cauchy problem to Schrodinger maps. In the process of study, we proved endpoint Strichartz estimates for the Schrodinger and Klein-Gordon equation adding angular regularity.

Research Products

• [Journal Article] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2011)
  • Author(s): Jun Kato, Tohru Ozawa
  • Journal Title: J. Math. Pures Appl Volume: 95 Pages: 48-71
  • Peer Reviewed
• [Journal Article] A new proof of long range scattering for critical nonlinear Schrodinger equations (2011)
  • Author(s): Jun Kato, Fabio Pusateri
  • Journal Title: Differential Integral Equations Volume: 24 Pages: 923-940
  • Peer Reviewed
• [Journal Article] Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications (2011)
  • Author(s): Jun Kato, Tohru Ozawa
  • Journal Title: J.Math.Pures Appl 95 Pages: 48-71
• [Journal Article] A new proof of long-range scattering for critical nonlinear schr-dinger equations (2011)
  • Author(s): Jun Kato, Fabio Pusateri
  • Journal Title: Differential Integral Equations 24 Pages: 923-940
• [Journal Article] Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications (2011)
  • Author(s): Jun Kato, Tohru Ozawa
  • Journal Title: J.Math.Pures Appl. Volume: 95 Pages: 48-71
  • Peer Reviewed
• [Journal Article] A new proof of long-range scattering for critical nonlinear Schrodinger equations (2011)
  • Author(s): Jun Kato, Fabio Pusateri
  • Journal Title: Differential and Integral Equations Volume: 24 Pages: 923-940
  • Peer Reviewed
• [Journal Article] A remark on global solutions to nonlinear Klein-Gordon equation with a quadratic nonlinearity in two space dimensions (2009)
  • Author(s): Jun Kato, Tohru Ozawa
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B14 Pages: 17-25
  • Peer Reviewed
• [Journal Article] A remark on global solutins to nonlinear Klein-Gordon equation with a quadratic nonlinearity in two space dimensions (2009)
  • Author(s): Jun Kato, Tohru Ozawa
  • Journal Title: RIMS Kokyuroku Bessatsu, B 14 Pages: 17-25
• [Presentation] 長距離型Hartree方程式に対する縮小写像の方法 (2012)
  • Author(s): 加藤淳
  • Organizer: 松山解析セミナー2012
  • Place of Presentation: 愛媛大学(招待講演)
  • Year and Date: 2012-02-03
• [Presentation] Navier-Stokes方程式の適切性に関する最近の話題について (2012)
  • Author(s): 加藤淳
  • Organizer: 平成23年度数学・数理科学と諸数学・産業との連携研究ワークショップ「乱流と流体方程式の解の特異性」
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2012-01-27
• [Presentation] Contraction mapping principle for the Hartree equation of the long range type (2012)
  • Organizer: 第29回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-01-25
• [Presentation] Contraction mapping principle for the Hartree equation of the long rangetype (2012)
  • Author(s): 加藤淳
  • Organizer: 第29回九州における偏微分方程式研究集会
  • Place of Presentation: 九州大学西新プラザ(招待講演)
  • Year and Date: 2012-01-25
• [Presentation] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2010)
  • Organizer: Analysis Seminar
  • Place of Presentation: Johns Hopkins University(Baltimore, USA)
  • Year and Date: 2010-09-20
• [Presentation] Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications (2010)
  • Author(s): Jun Kato
  • Organizer: Analysis Seminar
  • Place of Presentation: Johns Hopkins University (USA)
  • Year and Date: 2010-09-20
• [Presentation] A new approach to the derivation of asymptotic behavior on the small solution to the critical nonlinear Schrodinger equations (2010)
  • Organizer: Harmonic Analysis and PDE
  • Place of Presentation: Seoul National University(Seoul, Korea)
  • Year and Date: 2010-08-19
• [Presentation] A new approach to the derivation of asymptotic behavior ot the small solution to the critical nonlinear Schrodinger equations (2010)
  • Author(s): Jun Kato
  • Organizer: Harmonic Analysis and PDE
  • Place of Presentation: Seoul National University (South Korea)
  • Year and Date: 2010-08-19
• [Presentation] 角度方向の正則性とStrichartz型評価について (2009)
  • Author(s): 加藤淳
  • Organizer: 青葉山勉強会(第2回)「分散型方程式の解の正則性」
  • Place of Presentation: 東北大学
  • Year and Date: 2009-08-04
• [Presentation] 角度方向の滑らかさとStrichartz型評価について (2009)
  • Organizer: RIMS短期共同研究「非線形双曲型及び分散型方程式の解の挙動について」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-05-28
• [Presentation] 角度方向の滑らかさとStrichartz型評価について (2009)
  • Author(s): 加藤淳
  • Organizer: 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」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-05-26
• [Presentation] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2008)
  • Organizer: Asymptotics and Singularities in Nonlinear and Geometric Dispersive equations
  • Place of Presentation: BIRS(Banff, Canada)
  • Year and Date: 2008-08-28
• [Presentation] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2008)
  • Author(s): Jun Kato
  • Organizer: Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations
  • Place of Presentation: BIRS, Banff (Canada)
  • Year and Date: 2008-08-28
• [Presentation] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2008)
  • Author(s): 加藤淳
  • Organizer: Asymptotics and Singularities in Nonlinear and Geometric Dispersive Equations
  • Place of Presentation: BIRS, Banff, Canada
  • Year and Date: 2008-08-28
• [Presentation] Endpoint Strichartz estimates for the two dimensional Klein-Gordon equation and some applications (2008)
  • Organizer: RIMS研究集会「調和解析と非線形偏微分方程式」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-07-08
• [Presentation] Endpoint Strichartz estimates for the Klein-Gordon equation and the Schrodinger equation in two space dimensions (2008)
  • Author(s): Jun Kato
  • Organizer: RIMS研究集会「調和解析と非線型偏微分方程式」
  • Place of Presentation: 数理解析研究所(京都大学)
  • Year and Date: 2008-07-08
• [Presentation] Endpoint Strichartz estimates for the Klein-Gordon and the Schroinger equations in two space dimensions (2008)
  • Author(s): 加藤淳
  • Organizer: RIMS研究集会「調和解析と非線形偏微分方程式」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-07-08