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这个项目由两个部分组成：a）对磁性流体动力学方程和多相流的解决方案的大量时间行为的研究，以及对非线性术语对远处溶液行为的影响的研究。 更确切地说，频率空间中的非线性项会产生模式的某些混合，这些模式会引入长波，从而减慢衰减。 b）对圆上流体运动的类似物的研究，其稳定性和长时间的行为。 期望此处使用的方法可以扩展到三维球体。%%这些项目分析粘性流体方程的模型，这些模型包含非线性效应。 随着时间的流逝，兴趣集中在理解流体的行为上，一个目标是证明这种流体的运动比纯粹耗散性的流体运动所花费的时间更长。 这项研究可能会导致对湍流的更好理解，并可能在天气预测中找到应用。 ***