Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum

Abstract

In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum.

References in corpus (4)

• Global Wellposeness for the 3D inhomogeneous incompressible Navier-Stokes equations
• On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces
• Global well-posedness of the 1D compressible Navier-Stokes equations with constant heat conductivity and nonnegative density
• Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum