论文标题
在增强的BousSinesQ方程
On Enhanced Dissipation for the Boussinesq Equations
论文作者
论文摘要
在本文中，我们考虑了2D Boussinesq方程的稳定性和阻尼问题，其部分耗散在两个固定溶液的两个参数家族附近，其中包括COUETTE流量和静液压平衡。 在第一部分中，我们表明，对于无限周期通道中的线性化问题，如果任何扩散系数非零，则进化在渐近稳定。特别是，这比例如垂直扩散构成了弱条件。此外，我们研究了剪切流，静水平衡和部分耗散的相互作用。 在第二部分中，我们适应了Navier-Stokes问题中Bedrossian，Vicol和Wang使用的方法，并将它们与BousSinesQ方程的取消特性相结合，以建立小数据稳定性和增强的非线性Boussinesq问题的耗散结果，并充分消散。
In this article we consider the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow and hydrostatic balance. In the first part we show that for the linearized problem in an infinite periodic channel the evolution is asymptotically stable if any diffusion coefficient is non-zero. In particular, this imposes weaker conditions than for example vertical diffusion. Furthermore, we study the interaction of shear flow, hydrostatic balance and partial dissipation. In a second part we adapt the methods used by Bedrossian, Vicol and Wang in the Navier-Stokes problem and combine them with cancellation properties of the Boussinesq equations to establish small data stability and enhanced dissipation results for the nonlinear Boussinesq problem with full dissipation.
