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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2504.02669 |
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| _version_ | 1866916690518867968 |
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| author | Liang, Tao Li, Yongsheng Zhai, Xiaoping |
| author_facet | Liang, Tao Li, Yongsheng Zhai, Xiaoping |
| contents | In this paper, we investigate the stability threshold problem of the two-dimensional Navier-Stokes Boussinesq(NSB) equations in a finite channel $ \T \times [-1,1]$, focusing on the stability around the near Couette shear flow $ (U(y), 0)$, assuming the Navier slip boundary conditions are satisfied. In particular, when the initial data for the vorticity resides in an anisotropic Sobolev space of size $ O(\min \{ μ^{\frac{1}{2}}, ν^{\frac{1}{2}}\})$, and the initial perturbation of the temperature resides in an anisotropic Sobolev space of size $ O(\min \{ μ, ν\})$, we derive the nonlinear enhanced dissipation effect and the inviscid damping effect for the NSB system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel Liang, Tao Li, Yongsheng Zhai, Xiaoping Analysis of PDEs In this paper, we investigate the stability threshold problem of the two-dimensional Navier-Stokes Boussinesq(NSB) equations in a finite channel $ \T \times [-1,1]$, focusing on the stability around the near Couette shear flow $ (U(y), 0)$, assuming the Navier slip boundary conditions are satisfied. In particular, when the initial data for the vorticity resides in an anisotropic Sobolev space of size $ O(\min \{ μ^{\frac{1}{2}}, ν^{\frac{1}{2}}\})$, and the initial perturbation of the temperature resides in an anisotropic Sobolev space of size $ O(\min \{ μ, ν\})$, we derive the nonlinear enhanced dissipation effect and the inviscid damping effect for the NSB system. |
| title | Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.02669 |