Existence of energy-variational solutions to hyperbolic conservation laws
Analysis of PDEs
2022-11-23 v1
Abstract
We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions is convex and weakly-star closed. The existence of energy-variational solutions is proven via a suitable time-discretization scheme under certain assumptions. This general result yields existence of energy-variational solutions to the magnetohydrodynamical equations for ideal incompressible fluids and to the Euler equations in both the incompressible and the compressible case. Moreover, we show that energy-variational solutions to the Euler equations coincide with dissipative weak solutions.
Keywords
Cite
@article{arxiv.2211.12307,
title = {Existence of energy-variational solutions to hyperbolic conservation laws},
author = {Thomas Eiter and Robert Lasarzik},
journal= {arXiv preprint arXiv:2211.12307},
year = {2022}
}