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Wentzell–Freidlin Large Deviation Principle for Stochastic Convective Brinkman–Forchheimer Equations
Journal of Mathematical Fluid Mechanics ( IF 1.3 ) Pub Date : 2021-05-13 , DOI: 10.1007/s00021-021-00587-x
Manil T. Mohan

This work addresses some asymptotic behavior of solutions to stochastic convective Brinkman–Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to SCBF equations in a suitable Polish space. Then, the Wentzell–Freidlin type large deviation principle is derived using the well known results of Varadhan and Bryc. The large deviations for short time are also considered in this work. Furthermore, we study the exponential estimates on certain exit times associated with the solution trajectory of SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Wentzell–Freidlin type large deviations principle (LDP). This work also improves several LDP results available in the literature for tamed Navier–Stokes equations as well as Navier–Stokes equations with damping in bounded domains.



中文翻译:

随机对流Brinkman-Forchheimer方程的Wentzell-Freidlin大偏差原理

这项工作解决了随机对流Brinkman-Forchheimer(SCBF)方程在二维和三维有界域中被乘性高斯噪声扰动的解的一些渐近行为。使用Budhiraja和Dupuis的弱收敛方法,我们建立了Laplace原理,用于在合适的波兰空间中强力求解SCBF方程。然后,使用Varadhan和Bryc的众所周知的结果推导出Wentzell-Freidlin型大偏差原理。这项工作还考虑了短时间的大偏差。此外,我们研究了与SCBF方程的求解轨迹相关的某些退出时间的指数估计。使用收缩原理,我们从Wentzell-Freidlin型大偏差原理(LDP)的参考框架中研究出口时间的这些指数估计。这项工作还改进了文献中针对驯服的Navier-Stokes方程以及带界域阻尼的Navier-Stokes方程的一些LDP结果。

更新日期:2021-05-14
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