Joint French-Czech mathematics meeting

INSA-Lyon, November 29-30, 2018

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.