随机Navier-Stokes方程组来源于航空、生物与力学等领域，有着广泛的应用前景。本项目主要围绕Levy过程扰动的随机可压缩Navier-Stokes方程组展开研究，目标是建立该方程组的适定性理论、大偏差原理，研究内容包括解的存在性和唯一性、马尔科夫选择存在性、大偏差等问题。Levy过程扰动的随机可压缩Navier-Stokes方程组具有耦合性、退化性、强非线性性、跳跃等特点，理论研究具有挑战性。从已有的工作可以看出，解决这些问题需要探索新方法和新思路。本项目首先尝试用五层逼近方法、随机相对熵不等式、指数型能量估计来探索这些问题。然后力争创建独具特色的新方法，得到一般的理论，进而达到丰富和完善随机Navier-Stokes方程组理论体系的目的。因此研究Levy过程扰动的随机可压缩Navier-Stokes方程组具有重要的理论意义。

Stochastic Navier-Stokes equations are derived from the fields of aeronautics, biology and mechanics, and have a wide range of application prospects. In this project, we study the stochastic compressible Navier-Stokes equations with the Levy process. The purpose of this project is to establish the well-posedness and the large deviation principle of the equations. The contents include the existence and uniqueness of the solution, the existence of Markov selection, the large deviation principle and so on. The stochastic compressible Navier-Stokes equations with the Levy process have the characteristics of coupling, degeneracy, strong nonlinearity and jump. The theoretical research is challenging. From the existing work, it can be seen that solving these problems needs to explore new methods and new ideas. We first try to explore these problems by using the five-layer approximation method, the stochastic relative entropy inequality and the exponential energy estimates. Then we want to develop new methods to get the general theory, and then to enrich the mathematical theory of the stochastic Navier-Stokes equations. Therefore, the study of this project is important and meaningful.