$L^\infty$ solutions for a model of polytropic gas flow with diffusive entropy

TL;DR

This paper proves the global existence of bounded solutions for a polytropic gas flow model with diffusive entropy, using finite difference schemes and compensated compactness theory.

Contribution

It introduces a method to establish convergence of finite difference schemes for the model, including Lax-Friedrichs and Godunov schemes, ensuring solution existence.

Findings

Convergence of finite difference schemes to $L^ abla$ solutions.

Application of compensated compactness theory for gas flow models.

Establishment of global $L^ abla$ solutions for the model.

Abstract

We establish the global existence of $L^\infty$ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax-Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.