Mathematical Structure in Fluid Mechanics

流体力学的数学结构

基本信息

批准号：
0607953
负责人：
Alexis Vasseur
金额：
$ 12万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2006
资助国家：
美国
起止时间：
2006-09-01 至 2010-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0607953&HistoricalAwards=false
关键词：
Mathematical Structure Fluid Mechanics

项目摘要

VasseurDms-0607953 The investigator carries out a qualitative study of partialdifferential equations arising as models in fluid mechanics andchemistry. Understanding the properties of these models is afundamental challenge both in mathematics and science. Theregularity and stability of solutions are issues strongly relatedto nontrivial physical phenomena like turbulence and phasetransitions that are complex multiscale problems. Analyzingmathematical models of these phenomena often requires thedevelopment of novel tools encompassing techniques from analysis,applied mathematics, and stochastics. This project, whichaddresses both theoretical and applied issues, spans fromconservation laws to Navier-Stokes equations, kinetic equations,and motion of particles in fluids. It requires tools from thetheories of nonlinear partial differential equations, asymptoticanalysis, probability, and stochastics. The discovery of mathematical structure in physical modelsis of great importance for a deeper understanding of the physicalphenomena themselves. It gives also some hints of the range ofvalidity of the models. In this project, the investigatordevelops and studies new models involving couplings between fluidmechanics and physics far from equilibrium. This field hasimportant applications in science and engineering. For example,it models pollutants in a river or combustion of gasoline in anengine. The applied and mathematical challenges stem from thecomplexity of the phenomena.

VasseurDms-0607953 研究人员对作为流体力学和化学模型出现的偏微分方程进行定性研究。理解这些模型的属性是数学和科学领域的一项基本挑战。解的规律性和稳定性是与湍流和相变等复杂的多尺度问题等重要物理现象密切相关的问题。分析这些现象的数学模型通常需要开发包含分析、应用数学和随机学技术的新颖工具。该项目解决了理论和应用问题，涵盖从守恒定律到纳维-斯托克斯方程、动力学方程和流体中粒子的运动。它需要非线性偏微分方程、渐近分析、概率和随机理论的工具。物理模型中数学结构的发现对于更深入地理解物理现象本身具有重要意义。它还给出了模型有效性范围的一些提示。在这个项目中，研究人员开发和研究了涉及远离平衡的流体力学和物理学之间耦合的新模型。该领域在科学和工程中具有重要的应用。例如，它模拟河流中的污染物或发动机中汽油的燃烧。应用和数学挑战源于现象的复杂性。