Stability threshold for 2D shear flows of the Boussinesq system near Couette
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| Format: | Preprint |
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2020
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| _version_ | 1866916291229515776 |
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| author | Bian, Dongfen Pu, Xueke |
| author_facet | Bian, Dongfen Pu, Xueke |
| contents | In this paper, we consider the stability threshold for the shear flows of the Boussinesq system in a domain $\mathbb{T} \times \mathbb{R}$. The main goal is to prove the nonlinear stability of the shear flow $(U^S,Θ^S)=((e^{νt\partial_{yy}}U(y),0)^{\top},αy)$ with $U(y)$ close to $y$ and $α\geq0$. We separate two cases: one is $α\geq 0$ small scaling with the viscosity coefficients and the case without smallness of $α$ and fixed heat diffusion coefficient. The novelty here is that we don't require $μ=ν$ and only need to assume that $μ$ is scaled with $ν$ or fixed, where $μ$ is the inverse of the Reynolds number and $ν$ is the heat diffusion coefficient. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_02386 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Stability threshold for 2D shear flows of the Boussinesq system near Couette Bian, Dongfen Pu, Xueke Analysis of PDEs In this paper, we consider the stability threshold for the shear flows of the Boussinesq system in a domain $\mathbb{T} \times \mathbb{R}$. The main goal is to prove the nonlinear stability of the shear flow $(U^S,Θ^S)=((e^{νt\partial_{yy}}U(y),0)^{\top},αy)$ with $U(y)$ close to $y$ and $α\geq0$. We separate two cases: one is $α\geq 0$ small scaling with the viscosity coefficients and the case without smallness of $α$ and fixed heat diffusion coefficient. The novelty here is that we don't require $μ=ν$ and only need to assume that $μ$ is scaled with $ν$ or fixed, where $μ$ is the inverse of the Reynolds number and $ν$ is the heat diffusion coefficient. |
| title | Stability threshold for 2D shear flows of the Boussinesq system near Couette |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2012.02386 |