Relative entropy method for measure-valued solutions in natural sciences

Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek, Agnieszka Świerczewska-Gwiazda


We describe the applications of the relative entropy framework introduced in \cite{Daf}. In particular the 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.


Measure-valued solution; weak-strong uniqueness; scalar conservation laws

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