Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929378447851520 |
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| author | Liu, Ning Liu, Yanlin Zhang, Ping |
| author_facet | Liu, Ning Liu, Yanlin Zhang, Ping |
| contents | In this paper, we first establish the global existence and stability of solutions to 3-D classical Navier-Stokes equations $(NS)$ in an infinite cylindrical domain with large Fourier mode initial data. Then we extend similar result for 3-D anisotropic Navier-Stokes equations $(ANS).$ We remark that due to the loss of vertical viscosity in $(ANS),$ the construction of the energy functionals for $(ANS)$ is much more subtle than that of $(NS).$ Compared with our previous paper for $(NS)$, we improve the polynomial decay in $k$ for the Fourier coefficients of the solution to be exponential decay in $k$ here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain Liu, Ning Liu, Yanlin Zhang, Ping Analysis of PDEs In this paper, we first establish the global existence and stability of solutions to 3-D classical Navier-Stokes equations $(NS)$ in an infinite cylindrical domain with large Fourier mode initial data. Then we extend similar result for 3-D anisotropic Navier-Stokes equations $(ANS).$ We remark that due to the loss of vertical viscosity in $(ANS),$ the construction of the energy functionals for $(ANS)$ is much more subtle than that of $(NS).$ Compared with our previous paper for $(NS)$, we improve the polynomial decay in $k$ for the Fourier coefficients of the solution to be exponential decay in $k$ here. |
| title | Global stability of large Fourier mode for 3-D anisotropic Navier-Stokes equations in cylindrical domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.05329 |