论文标题
Couette附近Boussinesq系统的2D剪切流的稳定性阈值
Stability threshold for 2D shear flows of the Boussinesq system near Couette
论文作者
论文摘要
在本文中，我们考虑了域中BousSinesQ系统的剪切流的稳定性阈值，$ \ Mathbb {T} \ Times \ Times \ Mathbb {R} $。主要目标是证明剪切流$（u^s，θ^s）的非线性稳定性=（（（e^{νt\ partial_ {yy}} u（y）u（y），0）^{\ top}，αy）$，带有$ u（y）$（y）$接近$ y $和$ y $和$ y $和$ y $和$α\ geq0 $。我们将两种情况分开：一个是$α\ geq 0 $ small缩放率，具有粘度系数，而无小$α$和固定热扩散系数的情况。这里的新颖性是我们不需要$μ=ν$，只需要假设$μ$用$ν$或固定缩放，其中$μ$是雷诺数的倒数，而$ν$是热扩散系数。
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.
