Local smoothing estimates for hyperbolic and dispersive equations and applications

• Project/Area Number: 20540165
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Mie University
• Principal Investigator: HIDANO Kunio Mie University, 教育学部, 准教授 (00285090)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: Strichartz型評価式 / 波動方程式 / 局所平滑化評価式 / 非線形波動方程式 / 最大存在時間 / 時間大域解 / 初期値問題 / 適切性 / 時間空間評価式 / Abstract Strichartz型評価式 / 半線形波動方程式 / 初期・境界値問題 / 外部領域

Research Abstract

Abstract Strichartz estimates have been obtained for wave equations outside obstacles. As an application, the global (in time) existence of small solutions to semilinear wave equations with power-type nonlinear terms has been proved in 3-D domain outside obstacles.
Weighted space-time L^2 estimates have been also obtained for wave equations with space-time dependent variable coefficients. As an application, some new results on local (in time) wellposedness have been proved for quasilinear wave equations with low regularity radial data.

Research Products

• [Journal Article] On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles (2010)
  • Author(s): Kunio Hidano, Jason Metcalfe, Hart F.Smith, Christopher D.Sogge, Yi Zhou
  • Journal Title: Transactions of the American Mathematical Society Vol.362, No.5 Pages: 2789-2809
  • Peer Reviewed
• [Journal Article] On weighted Strichartz estimates and NLS for radial data in Sobolev spaces of negative indices (2010)
  • Author(s): Kunio Hidano
  • Journal Title: RIMS Kokyuroku Bessatsu Vol.22 Pages: 1-12
  • Peer Reviewed
• [Journal Article] On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles (2010)
  • Author(s): Kunio Hidano, 他4名
  • Journal Title: Transactions of the American Mathematical Society Volume: 362 Pages: 2789-2809
  • Peer Reviewed
• [Journal Article] On weighted Strichartz estimates and NLS for radial data in Sobolev spaces of negative indices (2010)
  • Author(s): Kunio Hidano
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: 22 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Small solutions to semi-linear wave equations with radial data of critical regularity (2009)
  • Author(s): Kunio Hidano
  • Journal Title: Revista Matematica Iberoamericana Vol.25, No.2 Pages: 693-708
  • Peer Reviewed
• [Journal Article] Small solutions to semi-linear wave equations with radial data of critical regularity (2009)
  • Author(s): Kunio Hidano
  • Journal Title: Revista Matematica Iberoamericana 25 Pages: 693-708
  • Peer Reviewed
• [Journal Article] Weighted HLS inequalities for radial functions and Strichartz estimates for wave and Schrodinger equations (2008)
  • Author(s): Kunio Hidano, Yuki Kurokawa
  • Journal Title: Illinois Journal of Mathematics Vol.52, No.2 Pages: 365-388
  • Peer Reviewed
• [Journal Article] Nonlinear Schrodinger equations with radially symmetric data of critical regularity (2008)
  • Author(s): Kunio Hidano
  • Journal Title: Funkcialaj Ekvacioj Vol.51, No.1 Pages: 135-147
  • Peer Reviewed
• [Journal Article] Nonlinear Schrodinger equations with radially symmetric data of critical regularity (2008)
  • Author(s): Kunio Hidano
  • Journal Title: Funkcialaj Ekvacioj 51巻1号 Pages: 135-147
  • Peer Reviewed
• [Journal Article] Weighted HLS inequalities for radial functions and Strichartz estimates for wave and Schrodinger equations
  • Author(s): Kunio Hidano, 他1名
  • Journal Title: Illinois Journal of Mathematics (掲載決定)
  • Peer Reviewed
• [Journal Article] Small solutions to semi-linear wave equations with radialdata of critical regularity
  • Author(s): Kunio Hidano
  • Journal Title: Revista Matematica Iberoamericana (掲載決定)
  • Peer Reviewed
• [Journal Article] On weighted Strichartz estimates and NLS for radialdata in Sobolev spaces of negative indices
  • Author(s): Kunio Hidano
  • Journal Title: RIMS Kokyuroku Bessatsu (掲載決定)
  • Peer Reviewed
• [Presentation] On almost global wellposedness for quasilinear wave equations with radial symmetry (2010)
  • Author(s): Kunio Hidano, Chengbo Wang, Kazuyoshi Yokoyama
  • Organizer: AMS 2010 Spring Western Section Meeting (Special Session on Harmonic Analysis and Partial Differential Equations)
  • Place of Presentation: University of New Mexico(米国ニューメキシコ州)
  • Year and Date: 2010-04-17
• [Presentation] 3次元準線形波動方程式のH^2\times H^1-初期値に対する球対称解について (2010)
  • Author(s): 肥田野久二男, Chengbo Wang, 横山和義
  • Organizer: 日本数学会年会(関数方程式分科会)
  • Place of Presentation: 慶応義塾大学矢上キャンパス
  • Year and Date: 2010-03-27
• [Presentation] 変数係数の波動方程式に対する重みっき時空L^2評式と準線型方程式の時間局所適切性 (2008)
  • Author(s): 肥田野, 久二男
  • Organizer: 非線形双曲型および分散型方程式の研究
  • Place of Presentation: 京都府京都市
  • Year and Date: 2008-06-19
• [Presentation] 変数係数の波動方程式に対する重みつき時空L^2評価式と準線型方程式の時間局所適切性 (2008)
  • Author(s): 肥田野久二男
  • Organizer: 非線形双曲型および分散型方程式の研究
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-05-26
• [Presentation] Weighted Strichartz estimates and well-posedness for nonlinear wave equations with low-regularity data (2008)
  • Author(s): 肥田野久二男
  • Organizer: 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications (Session on Qualitative Behavior of Solutions to Evolutionary PDE's)
  • Place of Presentation: University of Texas at Arlington(米国テキサス州)
  • Year and Date: 2008-05-19
• [Presentation] Weighted Strichartz estimates and well-posedness for nonlinear wave equations with low-regularity data (2008)
  • Author(s): 肥田野, 久二男
  • Organizer: 7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: アメリカ合衆国テキサス州
  • Year and Date: 2008-05-19
• [Remarks] ホームページ等
  • URL: http://xxx.yukawa.kyoto-u.ac.jp/abs/1004.3349