Instabilites in Fluid Motion

DMS-9500466 Friedlander Friedlander和Vishik最近的结果给出了定常Euler流线性不稳定的一个充分条件。建议在几个方向上扩大这项工作。弗里德兰德表明，对于包括欧拉方程在内的偏微分方程类，在某些谱条件下的线性不稳定性意味着非线性不稳定性。使用 振荡积分理论，建议将不稳定性准则推广到更复杂的磁流体动力学系统。 另一个研究方向是研究流体动力学时间周期问题的Floquet根向量系统的完备性。 这项工作的各个方面将与M.M.合作进行。 Vishik，W.施特劳斯和V.I.尤多维奇 流体运动的稳定性/不稳定性问题是近百年来备受关注的经典问题。它是气象学、海洋学、地球物理学、天体物理学和等离子体物理学研究的基础，这些物理现象受潜在的流体不稳定性控制。尽管历史悠久，但一些重要问题仍然悬而未决。建议通过研究描述流体流动的数学偏微分方程来增加我们对流体基本行为的理解。

DMS-9500466 Friedlander Recent results of Friedlander and Vishik give a sufficient condition for linear instability of a steady Euler flow. It is proposed to extend this work in several directions. Friedlander is showing that for classes of PDE, including the Euler equations, linear instability under certain spectral conditions implies nonlinear instability. Using the theory of oscillatory integrals it is proposed to extend the instability criteria to the more complicated system of magnetohydrodynamics. Another line of research is the study of the completeness of a system of Floquet root vectors for time periodic problems of fluid dynamics. Aspects of this work will be undertaken in collaboration with M.M. Vishik, W. Strauss and V.I. Yudovich. The question of stability/instability of fluid motion is a classical problem that has received much attention in the past 100 years. It is fundamental to studies in meteorology, oceanography, geophysics, astrophysics and plasma physics where physical phenomena are governed by the underlying fluid instabilities. Despite its long history, a number of important questions remain open. It is proposed to increase our understanding of the fundamental behaviour of fluids by studying the mathematical partial differential equations that describe fluid flow .