论文标题
Wentzell-Freidlin的大型对流Brinkman-Forchheimer方程的大偏差原理
Wentzell-Freidlin Large Deviation Principle for the stochastic convective Brinkman-Forchheimer equations
论文作者
论文摘要
这项工作解决了解决随机对流Brinkman-Forchheimer（SCBF）方程的某些渐近行为，这些方程在有限域中被乘法性高斯噪声扰动。使用Budhiraja和Dupuis的弱收敛方法，我们建立了在合适的波兰空间中对SCBF方程的强溶液的拉普拉斯原理。然后，使用Varadhan和Bryc的众所周知的结果得出了Wentzell-Freidlin大偏差原理。这项工作还考虑了短时间内的大偏差。此外，我们研究了与SCBF方程的溶液轨迹相关的某些退出时间的指数估计。使用收缩原理，我们研究了从弗雷德林 - 韦泽尔型大偏差原理的参考框架中退出时间的这些指数估计。这项工作还改善了驯服的Navier-Stokes方程的文献中可用的几种LDP结果以及在有限域中具有阻尼的Navier-Stokes方程。
This work addresses some asymptotic behavior of solutions to the stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to the SCBF equations in a suitable Polish space. Then, the Wentzell-Freidlin 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 the SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Freidlin-Wentzell type large deviations principle. This work also improves several LDP results available in the literature for the tamed Navier-Stokes equations as well as Navier-Stokes equations with damping in bounded domains.
