Relative energy functionals in fluid dynamics

We discuss several application of the concept of relative energy/entropy functional in th context of mathematical fluid dynamics. Applications to well-posedness problems, weak-strong uniqueness, stability of numerical schemes as well as stochastic PDE's modeling compressible fluid flows will be given. This talk is based on joint work with P.Bella, D.Breit, M.Hofmanova, M. Lewicka, and A.Novotny.