底部局部随机强迫的Rayleigh-Bénard convection
Rayleigh-Bénard convection with stochastic forcing localised near the bottom
AI总结：
本文证明了在无限Prandtl数regime下，当随机扰动作用于底部薄层且noise的amplitude足够大时，三维Rayleigh-Bénard convection的随机流会稳定到唯一的stationary measure。
摘要：
我们证明了在无限Prandtl数regime下，对于维持在顶部和底部的任意温度对，三维Rayleigh-Bénard convection的stochastic stability。假设非退化的随机扰动作用于与domain底部相邻的薄层中，我们证明了在两个无限方向上具有周期性的随机流稳定到一个唯一的stationary measure，前提是从任何初始状态至少有一个点可达。我们还证明了如果noise的amplitude足够大，则后者性质被满足。
英文摘要：
We prove stochastic stability of the three-dimensional Rayleigh-Bénard convection in the infinite Prandtl number regime for any pair of temperatures maintained on the top and the bottom. Assuming that the non-degenerate random perturbation acts in a thin layer adjacent to the bottom of the domain, we prove that the random flow periodic in the two infinite directions stabilises to a unique stationary measure, provided that there is at least one point accessible from any initial state. We also prove that the latter property is satisfied if the amplitude of the noise is sufficiently large.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
