No abstract

No abstract

The goal of this lecture series is to discuss the main ingredients of the mathematical theory describing the time evolution of a viscous, compressible, and heat conducting fluid. The principal topics can be specified as follows:

No abstract

We introduce the notion of relative entropy for the weak solutions to the compressible Navier-Stokes system. In particular, we show that any finite energy weak solution satisfies a relative entropy inequality with respect to any couple of smooth functions satisfying relevant boundary conditions. As a corollary, we establish the weak-strong uniqueness property in the class of finite energy weak solutions, extending thus the classical result of Prodi and Serrin to the class of compressible fluid flows.