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

这是一项研究可压缩和湍流气体流动中产生的物理现象的数学模型的建议。特别是，主要的研究人员将使用分析和数值工具来研究三维双曲型方程组解的不稳定性，涡丝的演化，利用齐次化理论从湍流中推导宏观输运量，以及流体力学和等离子体物理中方程组的弱解的性质。各种类型的物理现象都涉及含有旋涡的流动。每天都有龙卷风或洗澡水流入下水道。数学家研究这种涡旋运动的特性，是通过构造具有类似涡旋的解的简化方程组，然后使用解析和数值方法来预测这些解是如何随时间演变的。首席研究员将研究空气动力学和等离子体物理中出现的涡流模型。

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.