Well-posedness in critical spaces for the compressible Navier-Stokes   equations with density dependent viscosities
  In this paper, we prove the local well-posedness in critical Besov spaces for the compressible Navier-Stokes equations with density dependent viscosities under the assumption that the initial density is bounded away from zero. 
Qionglei Chen, Changxing Miao and Zhifei Zhang