Dynamical Systems Methods for Nonlocal, Nonautonomous and Nondissipative Systems

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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.