Asymptotics of solutions to the Navier-Stokes system in exterior domains

Abstract

We consider the incompressible Navier-Stokes equations with the Dirichlet boundary condition in an exterior domain of ${\mathbb{R}}^n$ with $n\ge 2$. We compare the long-time behaviour of solutions to this initial-boundary value problem with the long-time behaviour of solutions of the analogous Cauchy problem in the whole space ${\mathbb{R}}^n$. We find that the long-time asymptotics of solutions to both problems coincide either in the case of small initial data in the weak $L^n$-space or for a certain class of large initial data.

References in corpus (1)

• Global stability of vortex solutions of the two-dimensional Navier-Stokes equation

Cited by in corpus (1)

• On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains