关于几类随机流体力学的动力学行为的研究

本项目考虑Burgers系统和三维大气海洋方程在布朗运动，Lévy过程，分数布朗运动驱动下新的动力学行为，希望通过运用泛函分析，偏微分方程，随机分析等领域的思想方法和工具对他们进行一系列深入的研究来解释一些新的现象，或自然行为。该问题的研究，不仅对实际物理问题本身有重要的理论和实际意义，对深入理解和研究无穷维随机动力系统，也会有重要的帮助。具体的讲，本项目主要研究：(1) 随机Burgers系统整体吸引子的存在性。(2)Lévy过程驱动的三维随机大气海洋方程的随机吸引子。(3)Fractional Brownian Motion驱动的三维随机大气海洋方程的解的适定性及其密度。

The project considers Burgers system and three dimensional primitive equations of the large-scale ocean driven by stochastic noise ( Brownian motion, Lévy process, fractional Brownian motion ) to study new dynamical behavior . Using methods and techniques in functional analysis, partial differential equations and stochastic analysis,we hope to deeply study the above problems to explain new phenomenon, or their natural behavior. This research will not only have important theoretical and practical significance for physical problems, but also help us deeply understand and study the property of infinite dimensional stochastic dynamical systems. Specifically, the research of the project includs: (1) the global attractor of stochastic Burgers system; (2) stochastic attractor of 3-dimensional primitive equation of the large-scale ocean with Lévy jump; (3) 3-dimensional primitive equations of the large-scale ocean driven by fractional Brownian Motion: global well-posedness and density.