## 偏微分方程式セミナー（2014/12/15）: Stability of large solutions to the stationary Navier-Stokes equations in 3D multi-connected domains, 小薗英雄氏

2014年 　 12月 15日 16時 30分 ～ 2014年 　 12月 15日 17時 30分

In 3D multi-connected domains, it is still an open question whether there does
exist a solution of the stationary Navier-Stoeks equations with the inhomogeneous
boundary data whose total flux is zero.
The relation between the nonlinear structure of the equations and the
topological invariance of the domain plays an important role for solvability of this problem.
It is known that if the given boundary data data has a solenoidal
extension to the whole domain in such a way that the Leary-Fujita inequality is fulfilled,
then there exists at least one weak solution to the problem.
In this talk, we show an exponentially stability in $L^2$ of stationary
solutions which are close to the solenoidal extension in $L^3$ with the
Leary-Fujita inequality.
It should be noted that we need neither smallness of the stationary
solution nor that of the initial disturbance in $L^2$.
Our results is based on the joint work with Prof. Okabe and Dr. Kanbayashi.