标题： 二维Boussinesq系统在有限管道中接近库特流动的稳定性阈值 显示英文标题

标题： Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel

摘要： 本文研究了有限通道$\T \times [-1,1]$中二维纳维-斯托克斯-布辛涅斯克(NSB)方程的稳定性阈值问题，重点研究了近库埃特剪切流$(U(y), 0)$附近的稳定性，假设满足纳维滑移边界条件。 具体地，当涡量的初始数据位于大小为$O(\min \{ \mu^{\frac{1}{2}}, \nu^{\frac{1}{2}}\})$的各向异性Sobolev空间中，温度的初始扰动位于大小为$O(\min \{ \mu, \nu\})$的各向异性Sobolev空间中时，我们推导出NSB系统的非线性增强耗散效应和无粘阻尼效应。 显示英文摘要

摘要： 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 \{ \mu^{\frac{1}{2}}, \nu^{\frac{1}{2}}\})$, and the initial perturbation of the temperature resides in an anisotropic Sobolev space of size $ O(\min \{ \mu, \nu\})$, we derive the nonlinear enhanced dissipation effect and the inviscid damping effect for the NSB system.