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 Lp-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.

Keywords

compressible Navier-Stokes, vacuum, Cauchy problem, local existence

2010 Mathematics Subject Classification

35B45, 35M10, 35Q30, 76N10

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Published 21 December 2011