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 $\beta>4/3$.