论文标题
二维随机对流Brinkman-Forchheimer方程的占用度量的大偏差原理
Large deviation principle for occupation measures of two dimensional stochastic convective Brinkman-Forchheimer equations
论文作者
论文摘要
目前的工作关注的是二维随机对流Brinkman-Forchheimer（2D SCBF）方程，在$ \ r^{2} $的平滑界域中被白噪声（非退化）扰动。我们建立了与2D SCBF方程解决方案相关的马尔可夫半群（对于吸收指数$ r = 1,2,3 $）相关的两个重要属性，也就是说，不可约和强大的特性。这两种特性也意味着不变措施和奇迹性的独特性。然后，我们通过为大时（Donsker-Varadhan）提供了较大的偏差原理（LDP），讨论了2D SCBF方程的千古行为，该原理描述了指数融合的确切速率。
The present work is concerned about two-dimensional stochastic convective Brinkman-Forchheimer (2D SCBF) equations perturbed by a white noise (non degenerate) in smooth bounded domains in $\R^{2}$. We establish two important properties of the Markov semigroup associated with the solutions of 2D SCBF equations (for the absorption exponent $r=1,2,3$), that is, irreducibility and strong Feller property. These two properties implies the uniqueness of invariant measures and ergodicity also. Then, we discuss about the ergodic behavior of 2D SCBF equations by providing a Large Deviation Principle (LDP) for the occupation measure for large time (Donsker-Varadhan), which describes the exact rate of exponential convergence.
