### Antonin Novotny

#### Université du Sud Toulon-Var

#### Some properties of renormalized solutions to the families of transport equations and their consequences in the theory of compressible Navier-Stokes equations.

We shall investigate relations between renormalized
solutions of the transport and continuity equations with transporting
coefficient in Sobolev spaces and with possibly unbounded divergence.
These considerations lead to several statements which are not covered
by the DiPerna-Lions transport theory and its recent generaliazations
by Bianchini, Bonicatto, as for example, almost uniqueness or almost
compactness to the solutions to the pure transport equation. These
conclusions have interesting applications in the mathematical theory
of compressible fluids. We shall mention some of them.