随机偏微分方程是现代概率论最活跃的研究领域之一，对其深入细致研究具有重要的理论意义和应用价值。本项目拟研究流体力学中一类随机分数阶耗散偏微分方程的适定性和渐近性质，具体有以下3个方面:(1)Lévy过程驱动的随机分数阶耗散Leray-α模型和quasi-geostrophic方程鞅解和强解的存在唯一性，以及遍历性、大（中）偏差原理等渐近性质。(2)随机分数阶耗散Leray-α模型的随机吸引子的存在性及其维数刻画。(3)随机分数阶耗散Magneto-Hydrodynamic方程的适定性和遍历性。分数阶耗散方程由于耗散强度低，如何控制非线性项是研究的难点，需要在研究方法上有所创新。

Stochastic partial differential equation is one of the most active research fields in modern probability theory, a further detailed study for it has important theoretical significance and application value. This project aims to study the well-posedness and some asymptotic properties for a class stochastic partial differential equations with fractional dissipation in fluid mechanics. Specifically, following problems will be investigated in this project: (1) The existence and uniqueness of martingale solutions and strong solutions for stochastic Leray-α model and stochastic quasi-geotrophic equation with fractional dissipation driven by Lévy process, and the asymptotic properties such as ergodicity and large (moderate) deviation principle. (2) The existence and dimension characterization of random attractors for stochastic Leray-α model with fractional dissipation. (3) The well-posedness and ergodicity for stochastic Magneto-Hydrodynamic equation with fractional dissipation. Due to the low dissipation intensity of fractional dissipation equation, how to control the nonlinear term is the difficulty of the research, which needs some innovation in the research methods.