论文标题
温度对浮力驱动流体的稳定效果
The stabilizing effect of the temperature on buoyancy-driven fluids
论文作者
论文摘要
浮力驱动流体的Boussinesq系统伴随着浮力强迫的动量方程，并与温度的对流扩散方程式相结合。 BousSinesQ系统上的一个基本问题是在静水平衡附近的扰动方面的稳定性问题。当系统缺乏完全耗散时，这个问题可能非常困难。本文解决了仅垂直耗散和水平热扩散的二维BousSinesQ系统的稳定性问题。我们建立了非线性系统的稳定性，并为线性化系统提供精确的大型行为。本文介绍的结果揭示了浮力驱动流体的显着现象。也就是说，温度实际上可以平滑并稳定流体。如果不存在温度，则流体由仅垂直耗散的2D Navier-Stokes控制，其稳定性保持开放。 BousSinesQ系统中温度和速度之间的耦合和相互作用使这里研究了稳定性问题。从数学上讲，该系统可以简化为融合稳定的退化和阻尼的波动方程。
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on perturbations near the hydrostatic balance. This problem can be extremely difficult when the system lacks full dissipation. This paper solves the stability problem for a two-dimensional Boussinesq system with only vertical dissipation and horizontal thermal diffusion. We establish the stability for the nonlinear system and derive precise large-time behavior for the linearized system. The results presented in this paper reveal a remarkable phenomenon for buoyancy driven fluids. That is, the temperature actually smooths and stabilizes the fluids. If the temperature were not present, the fluid is governed by the 2D Navier-Stokes with only vertical dissipation and its stability remains open. It is the coupling and interaction between the temperature and the velocity in the Boussinesq system that makes the stability problem studied here possible. Mathematically the system can be reduced to degenerate and damped wave equations that fuel the stabilization.
