On entropy conservation for general systems of conservation laws
Tomasz D\k{e}biec
TL;DR
This paper explores conditions under which weak solutions of general conservation law systems conserve entropy, focusing on flux regularity and applications to nonlinear elasticity and Euler systems.
Contribution
It establishes sufficient regularity conditions for weak solutions to satisfy companion conservation laws in general systems.
Findings
Weak solutions satisfy companion laws under certain flux regularity.
Application framework for nonlinear elasticity and Euler systems.
Conditions for entropy conservation in complex systems.
Abstract
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be , , regular. We discuss applications of the general framework to nonlinear elasticity and compressible Euler system.
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Taxonomy
TopicsNavier-Stokes equation solutions · Geometric Analysis and Curvature Flows · Advanced Mathematical Physics Problems