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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16401 |
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Table of Contents:
- In this paper, we investigate the nonlinear stability and transition threshold for the 3D Boussinesq system in Sobolev space under the high Reynolds number and small thermal diffusion in $\mathbb{T}\times\mathbb{R}\times\mathbb{T} $. It is proved that if the initial velocity $v_{\rm in}$ and the initial temperature $ θ_{\rm in} $ satisfy $ \|v_{\rm in}-(y,0,0)\|_{H^{2}}\leq \varepsilonν, \|θ_{\rm in}\|_{H^{2}}\leq \varepsilonν^{2} $, respectively for some $ \varepsilon>0 $ independent of the Reynolds number or thermal diffusion, then the solutions of 3D Boussinesq system are global in time.