Dynamical Systems Methods for Nonlocal, Nonautonomous and Nondissipative Systems

研究方向：流体力学和地球物理流动领域的积分方程、常微分方程和偏微分方程非线性动力系统。研究重点是非局部、非自治和非耗散系统的动力系统方法的发展和应用。在非局部系统领域，研究者建议研究非局部积分项对Kuramoto-Sivashinsky和其他偏微分方程动力学的影响。在非自治系统中提出的工作将集中于地球物理流体粒子运动的研究。在非耗散系统领域，拟重点研究准地转方程和旋转浅水方程的动力学行为。提出的研究涉及流体系统中的复杂问题，特别是海洋和大气中的地球物理流体系统。这些问题的产生是由于需要对环境或全球变化有更好的科学认识。提出的研究是在微分方程和非线性现象的一般领域。

9704345 Duan The investigator plans to undertake a program of research in nonlinear dynamical systems modeled by integral, ordinary and partial differential equations, arising in fluid dynamics and geophysical flows. The research will focus on the development and application of dynamical systems methods for nonlocal, nonautonomous and nondissipative systems. In the area of nonlocal systems, the investigator proposes to study the effects of nonlocal integral terms on the dynamics of the Kuramoto-Sivashinsky and other partial differential equations. The proposed work in nonautonomous systems will concentrate on the study of geophysical fluid particle motions. In the area of nondissipative systems, the intended research is focused on dynamical behavior of the quasi-geostrophic equation and the rotating shallow water equations. The proposed research deals with complex problems in fluid systems, especially geophysical fluid systems in the oceans and the atmosphere. These problems are motivated by the need for better scientific understanding of the environment or global change. The proposed research is in the general area of differential equations and nonlinear phenomena.