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: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2025-0097 |
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| Summary: | 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. |
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| ISSN: | 2191-950X |