本项目主要研究时变区域上和低正则空间中非高斯噪声驱动无穷维随机动力系统的动力学。首次提出研究由纯跳Levy过程和分数布朗运动共同驱动的无穷维随机动力系统，研究包括三个方面：1）时变区域上Levy过程和分数布朗运动共同驱动的随机流体方程的动力学；2）低正则空间中Levy过程和分数布朗运动驱动的随机Strovsky方程的适定性和随机动力学研究；3）Levy过程和分数布朗运动共同驱动的空间分数次随机Boussinesq方程生成随机动力系统的基本理论。包括解的局部和整体适定性、时间和空间正则性、不变测度的存在唯一性、遍历性、随机动力系统的随机吸引子和随机不变流形的存在性和紧性等。通过对几类具有物理和流体背景的随机系统研究，分析随机系统的初值正则性、时变区域、非高斯噪声类型和分数阶的指数对随机发展方程生成的随机动力系统动力学的实质影响，改进和探索新的方法和技巧，并在研究中探索出现新现象。

The proposal is devoted to the study on dynamics of infinite-dimensional random dynamical systems driven by non-Gaussian noise on time-varying domain or lower-regularity space respectively. The proposal is firstly projected to study on the random dynamical systems driven by both Pure Levy noise and fractional Brownian motion, we focus on the following three parts: 1) Dynamics of stochastic fluid equation driven by both Levy noise and fractional Browmian motion on time-varyng domain, 2) Well-posedness and random dynamics of stochastic Ostrovsky equation driven by fractional Brownian motion or Levy noise in lower regularity space, and 3) basic theory of random dynamical systems generated by strochastic fractional Boussiesq equation driven by both Levy noise and fractional Brownian motion, which include the local well-posedness and global well-posedness, time and space regularity, the existence and uniqueness of the invariant measure, ergodicity, compactness of random dynamical systems, the existence of random attractor and random invaiant maniflod and so on. Based on the systematic research projected in this proposal, the effects on the solution of stochastic evolution equation can be provoded, include the regularity of initial values, time-varying domain, the type and property of non-Gaussian noise and the order of the fractional operators. Finaly, some new phenomenon and new technique are found or improved to deal with the difficulity occurred in the proposal research.