Viscous compressible homogeneous multi-fluids with multiple velocities:   barotropic existence theory
  We consider the model of viscous compressible homogeneous multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which arise during the proof of the existence theorems. 
Alexander Mamontov, Dmitriy Prokudin
math.AP