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

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 $\beta>4/3$.