On the asymptotic behaviour of solutions of the stationary Navier–Stokes equations in dimension 3

Abstract

In this paper, we address the problem of determining the asymptotic behaviour of the solutions of the incompressible stationary Navier–Stokes system in the full space, with a forcing term whose asymptotic behaviour at infinity is homogeneous of degree −3. We identify the asymptotic behaviour at infinity of the solution. We prove that it is homogeneous and that the leading term in the expansion at infinity uniquely solves the homogeneous Navier–Stokes equations with a forcing term which involves an additional Dirac mass. This also applies to the case of an exterior domain.