Mathematical Sciences: Aspects of Fluid Flows

数学科学：流体流动的各个方面

• 批准号: 9307497
• 负责人: Maria Schonbek
• 金额: $ 6万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307497&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Aspects; Fluid; Flows

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. ***

9307497 Schonbek本项目由两部分组成：a)研究磁流体力学和多相流方程解的大时间行为，以及研究非线性项对远场解行为的影响。更准确地说，频率空间中的非线性项将产生一些引入长波的模式的混合，从而减缓衰减；b)研究圆周上流体运动的类比，其稳定性和长时间行为。希望本文所用的方法可以推广到三维球面上。这些项目分析了包含非线性效应的粘性流体方程模型。人们的兴趣集中在了解流体在时间变大时的行为，其中一个目标是证明这种流体的运动比纯粹耗散的流体的运动需要更长的时间来减缓。这项研究可能有助于更好地理解湍流，并可能在天气预报中找到应用。***