二维随机Cahn-Hilliard-Navier-Stokes方程的中偏差原理

A moderate deviation principle of 2D stochastic Cahn-Hilliard-Navier-Stokes equation

有界区域上带乘性噪声的随机Cahn-Hilliard-Navier-Stokes方程是描述等温不可压缩二元流体运动的一类重要数学模型.由于乘性噪声的扰动,使得对方程解的研究变得复杂.通过构建新的近似系统和运用经典的弱收敛方法,证明了该系统的中偏差原理.

This paper considers a stochastic Cahn-Hilliard-Navier-Stokes equation with multiplicative noise in a bounded domain in R^(2),which is an important mathematical model to describe the motion of isothermal incompressible binary fluid.Due to perturbing of multiplicative noise,the system becomes more complicated.By constructing a new approximate system and using the classical weak convergence method,the moderate deviation principle of the system is proved.