Mathematical Sciences: Aspects of Fluid Flows

小行星9307497 本计画包含两个部分：a）研究磁流体力学与多相流方程解的大时间行为，以及非线性项对远场解行为的影响。 更确切地说，它将表明，在频率空间中的非线性项产生一些混合的模式，引入长波，将减缓衰减; B）对循环上流体运动的模拟、其稳定性和长时间行为的研究。 期望这里使用的方法可以扩展到三维球体。 这些项目分析包含非线性效应的粘性流体方程模型。 兴趣集中在理解的流体的行为，随着时间变大，一个目标是证明，这种流体的运动需要更长的时间比纯粹耗散的流体的运动减慢。 这项研究可能会导致更好地了解湍流，并可能在天气预报中找到应用。 ***

9307497 Schonbek This project consists of two parts: a) a study of the large time behavior of solutions to equations of magnetohydrodynamics and multiphase flow, and an investigation of the influence of the nonlinear terms on the behavior of the solutions in the far field. More precisely it will be shown that the nonlinear terms in frequency space produce some mixing of the modes which introduce long waves that will slow down the decay; b) a study of an analogue to a fluid motion on the circle, its stability and long time behavior. The expectation is that the methods used here can be extended to the three dimensional sphere.%%% These projects analyze models of viscous fluid equations which incorporate nonlinear effects. Interest is focused in understanding the behavior of the fluids as time gets large and one goal is to demonstrate that the motion of such fluids take longer in slowing down than the motion of fluids which are purely dissipative. This study could lead to a better understanding of turbulence and may find applications in weather prediction. ***