Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909491823378432 |
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| author | Shi, Jiajin Wang, Yi |
| author_facet | Shi, Jiajin Wang, Yi |
| contents | We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic perturbations, in particular, without zero-mass conditions. It is shown that if the composite wave strength and the initial perturbations are suitably small, then 3D Navier-Stokes system admits a unique global-in-time strong solution which time-asymptotically converges to the corresponding composite wave up to a time-dependent shift for planar viscous shock. Our proof is based on the $a$-contraction method with time-dependent shift and suitable weight function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations Shi, Jiajin Wang, Yi Analysis of PDEs We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic perturbations, in particular, without zero-mass conditions. It is shown that if the composite wave strength and the initial perturbations are suitably small, then 3D Navier-Stokes system admits a unique global-in-time strong solution which time-asymptotically converges to the corresponding composite wave up to a time-dependent shift for planar viscous shock. Our proof is based on the $a$-contraction method with time-dependent shift and suitable weight function. |
| title | Stability of composite Wave of Planar Viscous Shock and Rarefaction for 3D Barotropic Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.09321 |