Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data

TL;DR

This paper proves the global existence and uniqueness of classical solutions to the 2D barotropic compressible Navier-Stokes equations with vacuum and large initial data, under specific viscosity conditions.

Contribution

It establishes the first global well-posedness results for classical solutions with vacuum and large data in 2D under these viscosity assumptions.

Findings

Global existence and uniqueness of classical solutions

Solutions hold for vacuum states and large initial data

No restrictions on initial data size given viscosity conditions

Abstract

For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far field and with no restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is $\lambda = \rho^{\beta}$ with $\beta>4/3$.