Partial Differential Equations applied to fluid mechanics and related problems

偏微分方程应用于流体力学及相关问题

• 批准号: 0908196
• 负责人: Alexis Vasseur
• 金额: $ 27.43万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908196&HistoricalAwards=false
• 关键词: Partial; Differential; Equations; applied; fluid

This project is aimed at investigating regularity and possible blow-up of solutions to partial differential equations of fluid mechanics and related mathematical models. Understanding of properties of these models is a fundamental challenge both for mathematics and science. The regularity and stability of the solutions are strongly related to complex multiscale physical phenomena such as turbulence and phase transitions. A principal goal of this project is developing new techniques to tackle the problem of global regularity for super-critical systems including reaction-diffusion systems or the 3D Navier-Stokes system.This research program will make some significant progress in the fundamental understanding of the mathematics involved in fluid mechanics and chemistry. It will help also to train new graduate students in this important field. The discovery of mathematical structure in physical models will lead to a deeper understanding of the physical phenomena themselves. It will also provide some information about the limits of validity of the theoretical physical models that are used to describe physical phenomena.

本计画旨在探讨流体力学偏微分方程式及相关数学模型解的规律性与可能爆破。 理解这些模型的性质是数学和科学的根本挑战。解的正则性和稳定性与湍流和相变等复杂的多尺度物理现象密切相关。本项目的主要目标是开发新的技术来解决超临界系统的全局正则性问题，包括反应扩散系统或三维Navier-Stokes系统。本研究计划将在流体力学和化学中涉及的数学基础理解方面取得一些重大进展。 它还将有助于在这一重要领域培养新的研究生。物理模型中数学结构的发现将导致对物理现象本身更深入的理解。它还将提供一些关于用于描述物理现象的理论物理模型的有效性极限的信息。