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

TL;DR

This paper proves the local well-posedness of strong solutions to the isentropic compressible Navier-Stokes equations with vacuum initial data, notably without requiring compatibility conditions, advancing the mathematical understanding of these fluid dynamics equations.

Contribution

It establishes well-posedness without the common compatibility condition assumptions on initial data, a significant relaxation in the theory of compressible Navier-Stokes equations.

Findings

Well-posedness holds with vacuum initial data.

No compatibility condition needed on initial data.

Advances mathematical theory of compressible fluid flows.

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.