Mathematical Analysis of Vortex Dynamics and Waterwave Problem.
涡动力学和水波问题的数学分析。
基本信息
- 批准号:0433582
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2003
- 资助国家:美国
- 起止时间:2003-10-01 至 2005-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The PI proposes to study problems in three subjects of fluid dynamics: the motion of the interface of general two layered flow, the boundary layer problem, and the motion of water wave. The motion of the interface of general two layered fluid flow includes vortex sheet motion as a special case. In a recent work, the PI shows that arbitrarily specifying independent position and velocity data generally will yield no Sobolev class vortex sheet for any positive time. Some crucial assumptions in this work are: the fluids are inviscid, there is no surface tension, and the interface remains a regular surface at positive time. A problem of interest is therefore a well-posed model for the vortex sheet motion. The PI proposes to reintroduce viscosity into the fluids, and to understand the effect of the viscosity near the interface. This leads to the study of the zero viscosity limit of two layered viscous fluids. A related problem of both mathematical and practical importance is the boundary layer problem. The question is to find the zero viscosity limit of the incompressible Navier-Stokes flow in a domain with a fixed nonempty boundary. It is well-known that the difficulty is in the boundary layer, within which the normal velocity gradient generally becomes very large. The PI's approach is different from the usual one, in the sense that the PI will assume no knowledge of the possible limit equations. The PI proposes to analyze directly the Navier-Stokes flow, and to obtain the qualitative behavior of the boundary part and the interior part of the solutions of Navier-Stokes equation. The method will be from harmonic analysis. It is expected that the techniques and results developed in solving the boundary layer problem will provide insight in finding a well-posed model for the vortex sheet motion.The PI proposes to continue her study in the water wave problem. Recently, the PI proved the existence and uniqueness of solutions locally in time for the Water wave problem. The proposed research concentrates on issues relating to the long time behavior of the water wave: the global existenceand uniqueness of solutions, the lifespan of the water wave before singularity,and the singularity profile of the solution. The method will be from harmonic analysis and Clifford analysis.The methods and techniques developed by the PI in solving the water wave problemhas found applications in the vortex sheet problem. Success in this project will enhance our understanding of the wave motion, of the mixing of fluids, separation of boundary layers, generation of soundsand coherent structures in turbulence models.
PI建议研究流体动力学的三个学科:一般两层流的界面运动、边界层问题和水波运动。一般两层流体的界面运动作为特例包括涡片运动。在最近的一项工作中,PI表明,任意指定独立的位置和速度数据通常在任何正时间内都不会产生Soblev类涡片。这项工作中的一些关键假设是:流体是无粘性的,没有表面张力,界面在正时间保持规则的表面。因此,一个令人感兴趣的问题是一个适合涡片运动的模型。PI建议将粘度重新引入流体中,并了解界面附近粘度的影响。这就引出了两层粘性流体的零粘性极限的研究。一个既具有数学意义又具有实际意义的相关问题是边界层问题。问题是在具有固定非空边界的区域中求出不可压缩N-S流动的零粘性极限。众所周知,困难在于边界层,在边界层内,法向速度梯度通常会变得非常大。PI的方法不同于通常的方法,在某种意义上,PI将假定不知道可能的极限方程。PI建议直接分析N-S流动,得到N-S方程解的边界部分和内部部分的定性行为。该方法将从调和分析入手。期望在解决边界层问题中发展的技术和结果将为寻找适合涡片运动的模型提供帮助。PI建议继续她对水波问题的研究。最近,PI证明了水波问题及时局部解的存在唯一性。拟议的研究集中在与水波的长时间行为有关的问题上:解的全球存在性和唯一性、水波在奇点之前的寿命以及解的奇性轮廓。该方法将来自调和分析和Clifford分析。PI在解决水波问题中开发的方法和技术已在涡片问题中得到应用。这个项目的成功将加深我们对波动、流体混合、边界层分离、声音的产生和湍流模型中的相干结构的理解。
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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Sijue Wu其他文献
On the Motion of a Self-Gravitating Incompressible Fluid with Free Boundary
自由边界自引力不可压缩流体的运动
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:2.4
- 作者:
L. Bieri;Shuang Miao;S. Shahshahani;Sijue Wu - 通讯作者:
Sijue Wu
Wellposedness of the 2D full water wave equation in a regime that allows for non- $$C^1$$ interfaces
- DOI:
10.1007/s00222-019-00867-4 - 发表时间:
2019-03-23 - 期刊:
- 影响因子:3.600
- 作者:
Sijue Wu - 通讯作者:
Sijue Wu
Recent Progress in Mathematical Analysis of Vortex Sheets
涡流片数学分析最新进展
- DOI:
- 发表时间:
2003 - 期刊:
- 影响因子:0
- 作者:
Sijue Wu - 通讯作者:
Sijue Wu
Wellposedness and singularities of the water wave equations
水波方程的适定性和奇点
- DOI:
- 发表时间:
2015 - 期刊:
- 影响因子:0
- 作者:
Sijue Wu - 通讯作者:
Sijue Wu
Rigidity of acute angled corners for one phase Muskat interfaces
一相Muscat接口的锐角刚度
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:1.7
- 作者:
S. Agrawal;Neel Patel;Sijue Wu - 通讯作者:
Sijue Wu
Sijue Wu的其他文献
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{{ truncateString('Sijue Wu', 18)}}的其他基金
Mathematical Analysis of Fluid Free Boundary Problems
无流体边界问题的数学分析
- 批准号:
2153992 - 财政年份:2022
- 资助金额:
-- - 项目类别:
Standard Grant
Nonlinear Partial Equations and Applications
非线性偏方程及其应用
- 批准号:
1901739 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Analysis of the Water Wave Motion
水波运动的数学分析
- 批准号:
1764112 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Continuing Grant
Mathematical Analysis of the Water Wave Motion
水波运动的数学分析
- 批准号:
1101434 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Continuing Grant
Mathematical Analysis of the Water Wave Problem
水波问题的数学分析
- 批准号:
0800194 - 财政年份:2008
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Analysis of Vortex Sheet and Water Wave Motion
涡片与水波运动的数学分析
- 批准号:
0400643 - 财政年份:2004
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Analysis of Vortex Dynamics and Waterwave Problem.
涡动力学和水波问题的数学分析。
- 批准号:
0100204 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Standard Grant
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