Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations

Fuente: arXiv
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Main Authors: Peng, Yi, Shi, Xiaoding, Wu, Yuhang
Format: Preprint
Published: 2024
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_version_ 1866914726062063616
author Peng, Yi
Shi, Xiaoding
Wu, Yuhang
author_facet Peng, Yi
Shi, Xiaoding
Wu, Yuhang
contents In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to $H^{1}(\mathbb{R})$, $L^{2}(\mathbb{R})\cap L^{4}(\mathbb{R})$ and $L^{2}(\mathbb{R})$, provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to $L^{2}(\mathbb{R})$ can be arbitrarily large.
format Preprint
id arxiv_https___arxiv_org_abs_2403_15663
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations
Peng, Yi
Shi, Xiaoding
Wu, Yuhang
Analysis of PDEs
35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30
G.1.8
In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to $H^{1}(\mathbb{R})$, $L^{2}(\mathbb{R})\cap L^{4}(\mathbb{R})$ and $L^{2}(\mathbb{R})$, provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to $L^{2}(\mathbb{R})$ can be arbitrarily large.
title Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations
topic Analysis of PDEs
35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30
G.1.8
url https://arxiv.org/abs/2403.15663