IUMJ

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

Authors: Ching-Lung Lin, Gunther Uhlmann and Jenn-Nan Wang

Issue: Volume 60 (2011), Issue 6, 2093-2106

Abstract:

In this paper we are interested in the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is described 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 $\exp(-Ct^2 \log t)$ at infinity. Our proof is based on appropriate Carleman estimates.