Existence and uniqueness of global classical solutions to 3D isentropic compressible Navier-Stokes equations with general initial data

Abstract

In this paper we study the global existence and uniqueness of classical solutions to the Cauchy problem for 3D isentropic compressible Navier-Stokes equations with general initial data which could contain vacuum. We give the relation between the viscosity coefficients and the initial energy, which implies that the Cauchy problem under consideration has a global classical solution.