LOCAL EXISTENCE OF CLASSICAL SOLUTIONS TO THE TWO-DIMENSIONAL VISCOUS COMPRESSIBLE FLOWS WITH VACUUM

We consider the Cauchy problem of the barotropic compressible Navier-Stokes equations in 2D. The local existence of unique classical solution is established. We present some new elaborate estimates to bound the L-p-norm of the velocity u. The far field density is constant state, which could be either vacuum or non-vacuum. The initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large.