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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
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| 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 |