| 発表年月日 | 2015/08/17 |
|---|---|
| 発表テーマ | On decay rate estimates in subspaces for the Navier-Stokes equations |
| 会議名 | Mathematics for Nonlinear Phenomena |
| 開催地名 | Sapporo |
| 学会区分 | 国際学会 |
| 発表形式 | ポスター |
| 単独共同区分 | 単独 |
| 発表者・共同発表者 | Shuji Takahashi |
| 概要 | We consider the nonstationary incompressible Navier-Stokes equations in ${\bf R}^n\ (n\ge3)$.
Spatial decay rates of the solutions in the so called Serrin's class are shown, while decay rates of data are anisotropically prescribed. To consider anisotropic measurable functions, we recall the Lebesgue space equipped with the mixed norm. A weighted equation approach is applied here, that is, by multiplying anisotropically growing function to the equation, we estimate the weighted solution by the weighted and non-weighted data in the space with the mixed norm. We show that,even if the difference of decay rates in time between the solution and the external force is almost zero, we can take the difference of spatial decay rates of those close to 2 in a two-dimensional subspace and almost zero in the rest subspaces. |