Existence and Uniqueness of Strong Solutions for a Compressible   Multiphase Navier-Stokes Miscible Fluid-Flow Problem in Dimension n = 1
  We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the space derivative of the density, via a new kind of entropy. 
C. Michoski and A. Vasseur