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

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.

Asymptotic Stability of Combination of Contact Discontinuity with Rarefaction Waves for the One-Dimensional Viscous Micropolar Fluid Model

“…Here we used the same method as in [16] and combined with [50], then, we can complete the proof of Lemma 3.2. We omit the details for simplicity.…”