Regularity criteria and Liouville Theorem for 3D inhomogeneous Navier-Stokes flows with vacuum

Abstract

In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(\rho ,\mathbf{u})$ satisfies suitable conditions.