Well-posedness and ill-posedness for the nonlinear partial differential equations
| Project/Area Number |
25800069
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Tohoku University (2016)
Osaka City University (2015)
Chuo University (2013-2014) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 偏微分方程式 / 初期値問題 / 適切性および非適切性 / ベゾフ空間 / 非線形偏微分方程式 / 適切性 / 漸近挙動 / Besov空間 / 時間大域解 / シュレディンガー方程式 / 非適切性 / 移流拡散方程式 / Bugers 方程式 |
|---|
| Outline of Final Research Achievements |
This work is concerned with revealing and understanding the optimal initial condition for some nonlinear partial differential equations such as Navier-Stokes equations and Schrodinger equations. We studied the Navier-Stokes equations in the spaces of functions which have the bounded mean oscillation property, and also gave some initial condition for the equations with the Coriolis force. As to Schrodinger equations, we proved ill-posedness with quadratic non-linearity. It is also proved for the Burgers equation with the critical dissipation that small global solution tends to the Poisson kernel.
|
Report
(5 results)
Research Products
(40 results)
