Contents Online

# Communications in Mathematical Sciences

## Volume 10 (2012)

### Number 2

### Local existence of classical solutions to the two-dimensional viscous compressible flows with vacuum

Pages: 527 – 554

DOI: http://dx.doi.org/10.4310/CMS.2012.v10.n2.a6

#### Author

#### Abstract

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