On hyperbolic systems with entropy velocity covariant under the action of a group

TL;DR

This paper investigates hyperbolic conservation law systems with entropy velocity, establishing conditions for covariance under space-time transformation groups and illustrating with examples related to Galileo, Lorentz, and circular groups.

Contribution

It introduces a framework for hyperbolic systems with entropy velocity that are covariant under various transformation groups, including explicit constructions and examples.

Findings

Derived conditions for covariance under transformation groups

Constructed hyperbolic systems from null velocity data

Provided examples with Galileo, Lorentz, and circular groups

Abstract

For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of space-time transformations. These conditions naturally introduce a representation of the group in the space of states. We construct such hyperbolic system from the knowledge of data on the manifold of null velocity. We apply these ideas for Galileo, Lorentz and circular groups. We focus on particular non trivial examples for two by two systems of conservation laws.