Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929513634463744 |
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| author | Niu, Binqian Zhao, Weiren |
| author_facet | Niu, Binqian Zhao, Weiren |
| contents | In this paper, we improve the size requirement of the perturbations for the asymptotic stability of the Couette flow in stratified fluids governed by the two-dimensional Navier-Stokes-Boussinesq system. More precisely, the size of perturbed temperature is improved to $ν^{2/3}$ from $ν^{5/6}$ in the paper of Zhang and Zi [J. Math. Pure. Anal. 179:123-182 (2023)]. The idea is the quasi-linearization. The main system is decomposed into two or more equations: a good equation (might be linear) that carries the regularity and size of the initial data and some quasi-linear and nonlinear equations that contain the nonlinear part, which start from zero initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization Niu, Binqian Zhao, Weiren Analysis of PDEs In this paper, we improve the size requirement of the perturbations for the asymptotic stability of the Couette flow in stratified fluids governed by the two-dimensional Navier-Stokes-Boussinesq system. More precisely, the size of perturbed temperature is improved to $ν^{2/3}$ from $ν^{5/6}$ in the paper of Zhang and Zi [J. Math. Pure. Anal. 179:123-182 (2023)]. The idea is the quasi-linearization. The main system is decomposed into two or more equations: a good equation (might be linear) that carries the regularity and size of the initial data and some quasi-linear and nonlinear equations that contain the nonlinear part, which start from zero initial data. |
| title | Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.16216 |