Liouville theorems for the Stokes equations with applications to large time estimates

Abstract

We study Liouville theorems for the non-stationary Stokes equations in exterior domains in ${\mathbb{R}}^n$ under decay conditions for spatial variables. As applications, we prove that the Stokes semigroup is a bounded analytic semigroup on $L_{\sigma }^{\infty }$ of angle $\pi /2$ for $n\ge 3$. We also prove large time estimates for $n=2$ with zero net force.

26 pages