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

2018/06/10 by Liyun Zheng, Zheng, Liyun, Zhengzheng Chen +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1806.03617

openalex publication_date 2018/06/10 · openalex created_date 2018/06/13 · openalex updated_date 2026/07/28

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 L² energy method.

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