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
基本信息
- 批准号:0908196
- 负责人:
- 金额:$ 27.43万
- 依托单位:
- 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:
- 关键词:
项目摘要
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。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Alexis Vasseur其他文献
A bound from below for the temperature in compressible Navier–Stokes equations
- DOI:
10.1007/s00605-008-0021-y - 发表时间:
2008-08-07 - 期刊:
- 影响因子:0.800
- 作者:
Antoine Mellet;Alexis Vasseur - 通讯作者:
Alexis Vasseur
Alexis Vasseur的其他文献
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{{ truncateString('Alexis Vasseur', 18)}}的其他基金
Stability Theory for Systems of Hyperbolic Conservation Laws
双曲守恒定律系统的稳定性理论
- 批准号:
2306852 - 财政年份:2023
- 资助金额:
$ 27.43万 - 项目类别:
Standard Grant
DMS-EPSRC Collaborative Research: Stability Analysis for Nonlinear Partial Differential Equations across Multiscale Applications
DMS-EPSRC 协作研究:跨多尺度应用的非线性偏微分方程的稳定性分析
- 批准号:
2219434 - 财政年份:2022
- 资助金额:
$ 27.43万 - 项目类别:
Standard Grant
Regularity, Stability, and Turbulence in Fluid Flows
流体流动的规律性、稳定性和湍流
- 批准号:
1907981 - 财政年份:2019
- 资助金额:
$ 27.43万 - 项目类别:
Standard Grant
Stability of shocks and layers in Fluid Mechanics and related problems
流体力学中冲击和层的稳定性及相关问题
- 批准号:
1614918 - 财政年份:2016
- 资助金额:
$ 27.43万 - 项目类别:
Standard Grant
Partial Differential Equations applied to Oceanography and Classical Fluid Mechanics
偏微分方程应用于海洋学和经典流体力学
- 批准号:
1209420 - 财政年份:2012
- 资助金额:
$ 27.43万 - 项目类别:
Continuing Grant
Mathematical Structure in Fluid Mechanics
流体力学的数学结构
- 批准号:
0607953 - 财政年份:2006
- 资助金额:
$ 27.43万 - 项目类别:
Standard Grant
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