Existence, uniqueness and qualitative properties of solutions to Navier-Stokes equations for compressible fluids

We shall give an overview of some recent results on Navier-Stokes equations for compressible fluids. We will discuss existence of weak solutions for arbitrary large data, existence and uniqueness of strong solutions for small data, asymptotic behaviour of compressible flows past an obstacle and other topics. We will outline the principles of proofs of some of these results.

The lecture is intended for non-specialists. I will try to meet this uneasy goal.