Large-time behavior of the weak solution to 3D Navier-Stokes equations

Abstract

The weak solution to the Navier-Stokes equations in a bounded domain D⊂R 3 with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t≥0. In a bounded domain D the solution decays exponentially fast as t→∞ if the force term decays at a suitable rate. © 2012 Elsevier Ltd. All rights reserved.