Global axisymmetric solutions for Navier-Stokes equation with rotation uniformly in the inviscid limit
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908550404505600 |
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| author | Ko, Haram |
| author_facet | Ko, Haram |
| contents | We prove that the solutions to the 3D Navier-Stokes equation with constant rotation exist globally for small axisymmetric initial data, where the smallness is uniform with respect to the viscosity $ν\in [0,\infty)$. This expands the work by Guo, Pausader, and Widmayer \cite{GPW} which showed the global axisymmetric stability of rotation for 3D incompressible Euler's equation, to the viscous case, but for a single threshold that works for arbitrary viscosity. This is achieved by suitably adapting the dispersive framework established in \cite{GPW} to the Navier-Stokes setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_17528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global axisymmetric solutions for Navier-Stokes equation with rotation uniformly in the inviscid limit Ko, Haram Analysis of PDEs 35Q30, 76D03, 76D05, 76U05 We prove that the solutions to the 3D Navier-Stokes equation with constant rotation exist globally for small axisymmetric initial data, where the smallness is uniform with respect to the viscosity $ν\in [0,\infty)$. This expands the work by Guo, Pausader, and Widmayer \cite{GPW} which showed the global axisymmetric stability of rotation for 3D incompressible Euler's equation, to the viscous case, but for a single threshold that works for arbitrary viscosity. This is achieved by suitably adapting the dispersive framework established in \cite{GPW} to the Navier-Stokes setting. |
| title | Global axisymmetric solutions for Navier-Stokes equation with rotation uniformly in the inviscid limit |
| topic | Analysis of PDEs 35Q30, 76D03, 76D05, 76U05 |
| url | https://arxiv.org/abs/2409.17528 |