Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914771949846528 |
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| author | Vasseur, Alexis F. Yang, Jincheng |
| author_facet | Vasseur, Alexis F. Yang, Jincheng |
| contents | We provide an unconditional $L^2$ upper bound for the boundary layer separation of Leray-Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray-Hopf solution $u^ν$ and a fixed (laminar) regular Euler solution $\bar u$ with similar initial conditions and body force. We show an asymptotic upper bound $C \|\bar u\|_{L^\infty}^3 T$ on the layer separation, anomalous dissipation, and the work done by friction. This extends the previous result when the Euler solution is a regular shear in a finite channel. The key estimate is to control the boundary vorticity in a way that does not degenerate in the vanishing viscosity limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_05236 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain Vasseur, Alexis F. Yang, Jincheng Analysis of PDEs Fluid Dynamics 76D05, 35Q30 We provide an unconditional $L^2$ upper bound for the boundary layer separation of Leray-Hopf solutions in a smooth bounded domain. By layer separation, we mean the discrepancy between a (turbulent) low-viscosity Leray-Hopf solution $u^ν$ and a fixed (laminar) regular Euler solution $\bar u$ with similar initial conditions and body force. We show an asymptotic upper bound $C \|\bar u\|_{L^\infty}^3 T$ on the layer separation, anomalous dissipation, and the work done by friction. This extends the previous result when the Euler solution is a regular shear in a finite channel. The key estimate is to control the boundary vorticity in a way that does not degenerate in the vanishing viscosity limit. |
| title | Layer separation of the 3D incompressible Navier-Stokes equation in a bounded domain |
| topic | Analysis of PDEs Fluid Dynamics 76D05, 35Q30 |
| url | https://arxiv.org/abs/2303.05236 |