Stability of a Composite Wave of Two Seperate Strong Viscous Shock Waves for 1-D Isentropic Navier-Stokes System

TL;DR

This paper proves the stability of a composite wave formed by two viscous shock waves in the 1-D isentropic Navier-Stokes system, even with large wave strengths, given they start far apart.

Contribution

It establishes the stability of a composite wave of two viscous shocks with arbitrarily large strengths in the 1-D isentropic Navier-Stokes system.

Findings

Composite wave stability proven for large shock strengths

Stability holds when initial waves are sufficiently separated

Large time behavior characterized for the system

Abstract

In this paper, the large time behavior of solutions of 1-D isentropic Navier-Stokes system is investigated. It is shown that a composite wave consisting of two viscous shock waves is stable for the Cauchy problem provided that the two waves are initially far away from each other. Moreover the strengths of two waves could be arbitrarily large.