Global Entropy Solutions to Weakly Nonlinear Gas Dynamics

TL;DR

This paper establishes the existence, uniqueness, and bounded variation properties of entropy weak solutions for weakly nonlinear gas dynamics using a modified Glimm scheme and a priori estimates.

Contribution

It introduces a modified Glimm scheme and new a priori estimates to prove well-posedness and bounded variation of solutions in weakly nonlinear gas dynamics.

Findings

Existence of entropy weak solutions with bounded periodic initial data.

Uniqueness of solutions under the considered framework.

Uniform total variation bounds for the solutions.

Abstract

Entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics. Through a modified Glimm scheme, an approximate solution sequence is constructed, and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws, which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions.