GLOBAL WELL-POSEDNESS OF CLASSICAL SOLUTIONS TO THE CAUCHY PROBLEM OF TWO-DIMENSIONAL BAROTROPIC COMPRESSIBLE NAVIER-STOKES SYSTEM WITH VACUUM AND LARGE INITIAL DATA

The Cauchy problem for the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density is considered. When the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds, the global existence and uniqueness of strong and classical solutions is established. It should be remarked that there are no restrictions on the size of the data.