  In this article we describe the applications of the relative entropy
framework. In particular uniqueness of an entropy solution is proven for a
scalar conservation law, using the notion of measure-valued entropy solutions.
Further we survey recent results concerning measure-valued-strong uniqueness
for a number of physical systems - incompressible and compressible Euler
equations, compressible Navier-Stokes, polyconvex elastodynamics and general
hyperbolic conservation laws, as well as long-time asymptotics of the
McKendrick-Von Foerster equation.
