论文标题
两次尺度随机对流Brinkman-Forchheimer方程的大偏差
Large deviations for the two-time-scale stochastic convective Brinkman-Forchheimer equations
论文作者
论文摘要
对流Brinkman-Forchheimer（CBF）方程表征了在饱和多孔培养基中不可压缩流体流动的运动。在这项工作中，进行了两次和三维有限域中的两次随机对流Brinkman-Forchheimer（SCBF）方程的小噪声渐近线。更准确地说，我们为具有缓慢和快速的时间尺度的随机部分微分方程建立了一个温ZELL-Freidlin型大偏差原理，其中缓慢的组件是scbf方程，在两个和三个维度上受到小型多重高斯噪声的影响，快速成分是一种随机反应 - 反应 - 反应 - 反应 - 缩减方程。结果是通过Budhiraja和Dupuis（Khasminkii的时间离散化方法和停止时间参数）开发的变异方法（基于弱收敛方法）获得的。特别是，从这项工作中获得的结果对于二维随机Navier-Stokes方程也是如此。
The convective Brinkman-Forchheimer (CBF) equations characterize the motion of incompressible fluid flows in a saturated porous medium. The small noise asymptotic for the two-time-scale stochastic convective Brinkman-Forchheimer (SCBF) equations in two and three dimensional bounded domains is carried out in this work. More precisely, we establish a Wentzell-Freidlin type large deviation principle for stochastic partial differential equations with slow and fast time-scales, where the slow component is the SCBF equations in two and three dimensions perturbed by small multiplicative Gaussian noise and the fast component is a stochastic reaction-diffusion equation with damping. The results are obtained by using a variational method (based on weak convergence approach) developed by Budhiraja and Dupuis, Khasminkii's time discretization approach and stopping time arguments. In particular, the results obtained from this work are true for two dimensional stochastic Navier-Stokes equations also.
