Conservation Laws Invariant for Galileo Group; Cemracs Preliminary results

TL;DR

This paper introduces a class of hyperbolic conservation law systems invariant under Galileo transformations, leading to gas dynamics equations or novel exotic systems, based on natural physical and mathematical assumptions.

Contribution

It defines a new class of invariant hyperbolic systems under the Galileo group, expanding the understanding of conservation laws in physics.

Findings

Derivation of gas dynamics equations invariant under Galileo transformations

Identification of exotic systems consistent with the invariance

Framework for constructing invariant conservation law systems

Abstract

We propose a notion of hyperbolic system of conservation laws invariant for the Galileo group of transformations. We show that with natural physical and mathematical hypotheses, such a system conducts to the gas dynamics equations or to exotic systems that are detailed in this contribution to Cemracs 99.