Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain

Abstract

We study the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is modeled by the stationary Navier-Stokes equations in an exterior domain in ${\mathbb{R}}^n$ with $n\ge 2$. We will show that, under some assumptions, any nontrivial velocity field obeys a minimal decaying rate $\exp (-C{t}^2\log t)$ at infinity. Our proof is based on appropriate Carleman estimates.

16 pages