Stability and Uniqueness of Global Solutions to Euler Equations with Exothermic Reaction

TL;DR

This paper investigates the stability and uniqueness of global solutions to the Euler equations with exothermic reactions, establishing well-posedness and local features using a Lyapunov functional and front tracking method.

Contribution

It introduces a Lyapunov-type functional for the system and proves well-posedness and local properties of solutions for the Euler equations with exothermic reactions.

Findings

Established well-posedness of solutions

Analyzed local features of global solutions

Developed a Lyapunov-type functional

Abstract

We consider the Cauchy problems of a non-strictly hyperbolic system which describes the compressible Euler fluid with exothermic reaction. In this paper a Lyapunov-type functional is constructed for balance laws. By analysis of the flow generated by front tracking method, we prove the well-posedness theorems and present the local features of global solutions.