Structure stability of steady supersonic shear flow with inflow boundary conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916690389893120 |
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| author | Jiang, Song Zhou, Chunhui |
| author_facet | Jiang, Song Zhou, Chunhui |
| contents | We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption $0<L\ll1$, we prove that for any plane supersonic shear flow $\mathbf{U}^0=(μ(x_2),0)$, there exist smooth solutions near $\mathbf{U}^0$ to steady compressible Navier-Stokes equations in a 2-dimension domain $Ω=(0,L)\times (0,2)$. Moreover, based on the uniform-in-$\varepsilon$ estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure stability of steady supersonic shear flow with inflow boundary conditions Jiang, Song Zhou, Chunhui Analysis of PDEs We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption $0<L\ll1$, we prove that for any plane supersonic shear flow $\mathbf{U}^0=(μ(x_2),0)$, there exist smooth solutions near $\mathbf{U}^0$ to steady compressible Navier-Stokes equations in a 2-dimension domain $Ω=(0,L)\times (0,2)$. Moreover, based on the uniform-in-$\varepsilon$ estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations. |
| title | Structure stability of steady supersonic shear flow with inflow boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.10001 |