Decay of solutions of isentropic gas dynamics for large data

TL;DR

This paper investigates the decay behavior of solutions to the isentropic gas dynamics equations with large initial data, introducing a new method involving a global attractor and a modified Godunov scheme.

Contribution

It presents a novel approach to analyze decay for large data by proving the existence of a global attractor in isentropic gas dynamics.

Findings

Existence of a global attractor for large initial data

Decay of solutions established for large data

Introduction of a modified Godunov scheme for approximation

Abstract

In this paper, we are concerned with the Cauchy problem for isentropic gas dynamics. Through the contribution of many researchers such as Lax, P. D., Glimm, J., DiPerna, R. J. and Liu, T. P., the decay of solutions was established. They treated with initial data with the small total variation. On the other hand, the decay for large initial data has been open for half a century. Our goal is to provide a new method to analyze this problem. We prove the existence of a global attractor, which yields a decay of solutions for large data. To construct approximate solutions, we introduce a modified Godunov scheme.