Sobolev regular solutions for the incompressible Navier\u2013Stokes equations in higher dimensions: asymptotics and representation formulae

Abstract

In this paper, we consider the steady incompressible Navier–Stokes equations in a smooth bounded domain Omega subset mathbb R^n with the dimension nge 3. We first establish asymptotic expansion formulae of Sobolev regular finite energy solutions in Omega. In the second part of this paper, explicit representation formulae of Sobolev regular solutions are showed in the regular polyhedron Omega :=[0,T]^n.