Asymptotic stability of planar rarefaction wave to a multi-dimensional two-phase flow

Shu Wang; Yixuan Zhao

doi:10.3934/dcdsb.2022091

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2023, Volume 28, Issue 1: 623-647. Doi: 10.3934/dcdsb.2022091

This issue Previous Article On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis Next Article Boundary preserving explicit scheme for the Aït-Sahalia mode

Asymptotic stability of planar rarefaction wave to a multi-dimensional two-phase flow

Shu Wang and
Yixuan Zhao^,

Faculty of Science, Beijing University of Technology, Beijing 100124, China

^* Corresponding author: Yixuan Zhao
^* Corresponding author: Yixuan Zhao

Received: November 30, 2021

Early access: May 2022

Published: January 2023

The work is supported by National Natural Science Foundation of China (11601021, 11831003, 11771031, 12171111), the Science and Technology Project of Beijing Municipal Education Commission (KZ202110005011) and Project for University Key Young Teacher by Education of Henan Province (No.2021GGJS158)

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Abstract

We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in $ H^3 $. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method.

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Mathematics Subject Classification: Primary: 35Q30, 35Q31, 76n06, 76T06.

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