非牛顿流体力学反映了在给定温度和压强下应力与速度不再满足线性关系的流体运动。非牛顿流体在石油工业、生物工程、地质学及血液流变学等领域都有着广泛的应用。目前有关非牛顿流的研究成果主要集中在整数阶、确定性方程(或方程组)，然而，由于随机偏微分方程和分数阶偏微分方程具有更鲜明的物理背景和研究前景，因此对于随机非牛顿流和具有分数阶导数的非牛顿流的研究具有重要的物理意义和现实意义。本项目主要研究随机非牛顿流及其相关方程组,拟通过偏微分方程经典理论结合随机分析和调和分析的方法解决以下问题：随机非牛顿流的无粘极限、分数阶Boussinesq Approximation模型（非牛顿流方程与温度方程构成的耦合方程组）解的适定性以及长时间行为、随机分数阶Boussinesq Approximation模型无穷维动力系统的长时间行为。本项目不仅具有主流性、前沿性，更具有广泛的应用前景。

Non-Newtonian fluid mechanics reflect that constitutive.equation of fluid between stress tensor and velocity no longer satisfy the linear relationship at given temperature and pressure. There is a wide range of applications in petroleum industry, biomechanics, geology, hemorheology, and so on. The main research results of non-Newtonian fluid concentrate on integer order deterministic equations. However, due to more distinct physical background and research prospects for stochastic PDE and fractional PDE. It has important physical and practical significance to study stochastic non-Newtonian fluid and non-Newtonian fluid with fractional derivative. This project mainly studies the stochastic non-Newtonian and correlation equations. We hope to solve the following issues through the classic theories of PDE, the method of random analysis and harmonic analysis : the inviscid limit of stochastic non-Newtonian;the well-posedness and the long time behavior of solution to fractional Boussinesq Approximation;the infinite dimensional dynamical system for stochastic fractional Boussinesq Approximation.This project not only has the mainstream, frontier, but also has more extensive application prospect.