## 偏微分方程式セミナー(2014/6/2)：On Long-time asymptotics of the Navier-Stokes flows in a two-dimensional exterior domain, 前川泰則氏 (東北大学)

2014年 　 6月 2日 16時 30分 ～ 2014年 　 6月 2日 17時 30分

We consider the incompressible Navier-Stokes equations in a two-dimensional
exterior domain $\Omega$, with no-slip boundary conditions.
Our initial data are of the form $u_0=\alpha \Theta_0+v_0$, where $\alpha\in \R$, $\Theta_0$ is the Oseen vortex with unit circulation at infinity,
and $v_0$ is a solenoidal perturbation belonging to $(L^2(\Omega))^2$.
We show that the solution behaves asymptotically in time like the self-similar Oseen
vortex with circulation $\alpha$, when $\alpha$ is sufficiently small. This is a global
stability result, in the sense that the perturbation $v_0$ can be arbitrarily large.
This talk is mainly based on a joint work with Thierry Gallay (Grenoble, France).