Abstract
We describe the applications of the relative entropy framework introduced in [10]. 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.
Citation
Tomasz Dębiec. Piotr Gwiazda. Kamila Łyczek. Agnieszka Świerczewska-Gwiazda. "Relative entropy method for measure-valued solutions in natural sciences." Topol. Methods Nonlinear Anal. 52 (1) 311 - 335, 2018. https://doi.org/10.12775/TMNA.2018.027