Levy 过程驱动的随机偏微分方程遍历性的研究

Stochastic partial differential equation (SPDE) is one of the most important and hottest research topics of stochastic analysis, espically which are closedly related to hydrodynamics. Our main focuses are on the following problems will be investigated in this project: (1) Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations driven by Levy process. When characteristic measure is infinity,the relation of two stationary measures will be established.In order to study ergodicity of solutions, functional inequalities will be presented.(2)The existence of martingale solution and the existence of stationary for stochastic Prouse model driven by Levy process.We will study the convergence rate of the solution, exponential convergence and fuctional inequalities.The existence and uniqueness for stochastic dissipative equation driven by stable process, and some interesting properties of solutions for stochastic dissipative equation driven by stable process.

随机偏微分方程是随机分析研究的前沿领域，尤其对涉及流体力学等有深刻物理背景的随机偏微分方程的研究，既有重要的理论价值，又有实际意义。本项目研究的问题有：(1) 可乘Levy 过程驱动的三维Navier-Stokes 方程鞅解的存在性及Markov 选择的存在性。并进一步研究在特征测度是无限时，两类平稳测度的联系。以平稳测度为参考测度，建立相应的泛函不等式，为研究解的遍历性提供工具.(2) Levy过程驱动的随机Prouse模型鞅解及稳定解的存在性、解的收敛速度、指数收敛性及泛函不等式等;研究可加stable 过程驱动的随机耗散方程解的存在唯一性以及解的遍历性。

随机偏微分方程是随机分析研究的前沿领域，尤其对涉及流体力学等有深刻物理背景的随机偏微分方程的研究，既有重要的理论价值，又有实际意义。本项目研究的问题有：(1) 可乘Levy 过程驱动的三维Navier-Stokes 方程鞅解的存在性及Markov 选择的存在性。并进一步研究在特征测度是无限时，两类平稳测度的联系。以平稳测度为参考测度，建立相应的泛函不等式，为研究解的遍历性提供工具.(2) Levy过程驱动的随机Prouse模型鞅解及稳定解的存在性、解的收敛速度、指数收敛性及泛函不等式等;研究可加stable 过程驱动的随机耗散方程解的存在唯一性以及解的遍历性。