Asymptotic stability of a composite wave for the one-dimensional compressible micropolar fluid model without viscosity

TL;DR

This paper proves the asymptotic stability of a composite wave formed by a viscous contact wave and two rarefaction waves in a one-dimensional compressible micropolar fluid model without viscosity, using an elementary energy method.

Contribution

It establishes the stability of a specific wave pattern in a non-viscous micropolar fluid model, extending understanding of wave behavior without viscosity effects.

Findings

The composite wave is asymptotically stable under small initial perturbations.

The stability is proved using an elementary $L^2$ energy method.

The result applies to solutions with different far-field states.

Abstract

We are concerned with the large time behavior of solutions to the Cauchy problem of the one-dimensional compressible micropolar fluid model without viscosity, where the far-field states of the initial data are prescribed to be different. If the corresponding Riemann problem of the compressible Euler system admits a contact discontinuity and two rarefaction waves solutions, we show that for such a non-viscous model, the combination of the viscous contact wave with two rarefaction waves is time-asymptotically stable provided that the strength of the composite wave and the initial perturbation are sufficiently small. The proof is given by an elementary $L^2$ energy method.