Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity

This article shows time-asymptotic nonlinear stability of rarefaction wave to the Cauchy problem for the one-dimensional relaxed compressible Navier-Stokes equations with density-dependent viscosity. We prove that the solution to this typical system tends time-asymptotically to the rarefaction wave....

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Main Author: Zhang Nangao
Format: Article
Language:English
Published: De Gruyter 2025-08-01
Series:Advances in Nonlinear Analysis
Subjects:
Online Access:https://doi.org/10.1515/anona-2025-0097
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author Zhang Nangao
author_facet Zhang Nangao
author_sort Zhang Nangao
collection DOAJ
description This article shows time-asymptotic nonlinear stability of rarefaction wave to the Cauchy problem for the one-dimensional relaxed compressible Navier-Stokes equations with density-dependent viscosity. We prove that the solution to this typical system tends time-asymptotically to the rarefaction wave. For this, we technically construct the correction function Sˆ(x,t)\hat{S}\left(x,t), which means that S±{S}_{\pm } can be non-zero. The proof is accomplished by virtue of energy estimates.
format Article
id doaj-art-cef3a0514edc4fe8a80981dc38afb446
institution Kabale University
issn 2191-950X
language English
publishDate 2025-08-01
publisher De Gruyter
record_format Article
series Advances in Nonlinear Analysis
spelling doaj-art-cef3a0514edc4fe8a80981dc38afb4462025-08-20T03:44:06ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-08-011411116115910.1515/anona-2025-0097Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosityZhang Nangao0Research Center for Applied Mathematics and Interdisciplinary Sciences, School of Mathematics and Statistics, Wuhan Textile University, Wuhan 430200, ChinaThis article shows time-asymptotic nonlinear stability of rarefaction wave to the Cauchy problem for the one-dimensional relaxed compressible Navier-Stokes equations with density-dependent viscosity. We prove that the solution to this typical system tends time-asymptotically to the rarefaction wave. For this, we technically construct the correction function Sˆ(x,t)\hat{S}\left(x,t), which means that S±{S}_{\pm } can be non-zero. The proof is accomplished by virtue of energy estimates.https://doi.org/10.1515/anona-2025-0097compressible navier-stokes equationsrarefaction wavecorrection functionenergy estimates35q3535q6076n3076w05
spellingShingle Zhang Nangao
Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
Advances in Nonlinear Analysis
compressible navier-stokes equations
rarefaction wave
correction function
energy estimates
35q35
35q60
76n30
76w05
title Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
title_full Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
title_fullStr Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
title_full_unstemmed Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
title_short Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity
title_sort stability of rarefaction wave for relaxed compressible navier stokes equations with density dependent viscosity
topic compressible navier-stokes equations
rarefaction wave
correction function
energy estimates
35q35
35q60
76n30
76w05
url https://doi.org/10.1515/anona-2025-0097
work_keys_str_mv AT zhangnangao stabilityofrarefactionwaveforrelaxedcompressiblenavierstokesequationswithdensitydependentviscosity