Decay rate of solutions of Navier–Stokes equations in 3-dimensional half space

Abstract

In this article, we derive the L 2 spatial decay rate of a weak solution of the incompressible flow in the half space. When the half space (or some other fluid region with boundary) is concerned, pressure estimate is main obstacle since we do not have enough information of the pressure on the boundary. In this paper, we give an idea which does not require any pressure information on the boundary, and we hope that our idea could be applied to other problems such as exterior domain problem.