Sobolev regular solutions for the incompressible Navier–Stokes 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 Ω ⊂ Rn with the dimension n≥ 3. We first establish asymptotic expansion formulae of Sobolev regular finite energy solutions in Ω. In the second part of this paper, explicit representation formulae of Sobolev regular solutions are showed in the regular polyhedron Ω : = [0 , T] n.