Mathematical Sciences: Nonlinear Phenomena in Fluid Dynamicsand Related P.D.E.'s Theory, Asymptotics and Numerical Computation

点击翻译按钮获取中文摘要

This is a proposal to study mathematical models of physical phenomena arising in the flow of compressible and turbulent gases. In particular, the principal investigator will use analytical and numerical tools to investigate the instability of solutions of nonlinear systems of hyperbolic equations in three dimensions, the evolution of vortex filaments, the derivation of macroscopic transport quantities from turbulent flows using techniques of homogenization theory, and the properties of weak solutions of systems of equations from fluid dynamics and plasma physics. Various types of physical phenomena involve flows containing vortices. Everyday examples of vortices are tornadoes or the bath water as it goes down the drain. Mathematicians study the properties of such vortex motions by constructing simplified sets of equations that have "vortex-like" solutions and then using analytical and numerical methods to predict how these solutions evolve in time. The principal investigator will examine models of vortex flows that arise in aerodynamics and plasma physics.