Global classical solution to the Cauchy problem of 2D baratropic compressible Navier-Stokes system with large initial data

Abstract

For periodic initial data with initial density, we establish the global existence and uniqueness of strong and classical solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is $\lam=\rho^{\b}$ with $\b>1.$