On Liouville-type theorem for the stationary compressible Navier–Stokes equations in $ \mathbb{R}^{3} $

Abstract

In this paper, we study the Liouville-type theorem for the stationary barotropic compressible Navier–Stokes equations in $ \mathbb{R}^{3} $. Based on a fairly general framework of a kind of local mean oscillations integral and Morrey spaces, we prove that the velocity and the density of the flow are trivial without any integrability assumption on the gradient of the velocity.

Keywords

• liouville-type theorem
• compressible navier–stokes equaitons
• barotropic
• local mean oscillations integral
• morrey spaces