geometric structure of nonlinearity and singularity of solutions for wave equations
Project/Area Number |
22740088
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Single-year Grants |
Research Field |
Basic analysis
|
Research Institution | Nagoya University |
Principal Investigator |
KOTARO Tsugawa 名古屋大学, 多元数理科学研究科, 准教授 (70402451)
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
Keywords | 分散型方程式 / 非線形 / 偏微分方程式 / 慨周期関数 / 準周期関数 / 適切性 / シュレディンガー方程式 / ディラック方程式 / 関数方程式 / 初期値問題 |
Research Abstract |
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.
|
Report
(4 results)
Research Products
(21 results)