Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
基本信息
- 批准号:RGPIN-2014-06461
- 负责人:
- 金额:$ 1.31万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2016
- 资助国家:加拿大
- 起止时间:2016-01-01 至 2017-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
I propose to study the regularity of solutions for several representative partial differential equations in mathematical fluid mechanics.
Equations from fluid mechanics have always played an important role in the development of the theory of partial differential equations. Among the many open problems these equations present, one of the most important is their “well-posedness" regarding the existence and uniqueness of the solutions. The key to settling the well-posedness problem is to understand how the solutions can stay regular or form finite-time singularities. The significance of this problem is two-fold. From the mathematical point of view, regularity (or lack thereof) of solutions is the very first and most fundamental issue to be settled in any theory of partial differential equations; from the physical point of view, regularity of solutions directly relates to the validity of the equations as mathematical models for physical phenomena.
There are three major obstacles to successful mathematical analysis of equations from mathematical fluid mechanics: nonlinear terms, nonlocal operators, and coupling between unknown quantities. These difficulties have inspired the invention of several new methods and techniques for partial differential equations in recent years. However the progress is still far from satisfactory.
I plan to contribute to the theory of partial differential equations through detailed study of four representative systems: the two-dimensional generalized magnetohydrodynamical (GMHD) equations, the Euler-Poincare equations, a one-dimensional nonlinear nonlocal system, and the Onsager model for liquid crystals. These equations are chosen to achieve a balance of difficulty/impact and accessibility. On one hand, all four exhibit most, if not all, of the three difficulties in mathematical fluid mechanics: nonlinearity, nonlocality, and coupling. As a consequence, progress in the study of these equations would shed light on the study of other fluid mechanical equations. Furthermore, as many mathematical models in chemistry, biology, and engineering are derived using ideas from fluid mechanics, the proposed research will also have impact on those fields. On the other hand, there is evidence that the well-posedness problem of these systems, though still open, are among the more tractable ones in the many open problems in mathematical fluid mechanics. Therefore, these equations are ideal for the training of HQP.
The outcome of the proposed research will significantly improve our understanding of nonlinearity, nonlocality, and coupling in partial differential equations and will shed light on the study of a wide variety of equations from not only fluid mechanics but also other fields such as mathematical biology. It will also contribute to our understanding of turbulence. Progress in the proposed research will be of interest to both the partial differential equations community and the fluid mechanics community. Part of the proposed research will also draw attention from the community of nonlinear functional analysis. The proposed research will benefit from existing and potential national and international collaborations. Through working on the proposed projects, HQP will receive comprehensive training in partial differential equations, harmonic analysis, nonlinear functional analysis, fluid mechanics, and scientific computing.
本文拟研究数学流体力学中几个具有代表性的偏微分方程解的正则性。
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Yu, Xinwei其他文献
Quantifying lipid contents in enveloped virus particles with plasmonic nanoparticles.
- DOI:
10.1002/smll.201402184 - 发表时间:
2015-04 - 期刊:
- 影响因子:13.3
- 作者:
Feizpour, Amin;Yu, Xinwei;Akiyama, Hisashi;Miller, Caitlin M.;Edmans, Ethan;Gummuluru, Suryaram;Reinhard, Bjoern M. - 通讯作者:
Reinhard, Bjoern M.
Dressing up Nanoparticles: A Membrane Wrap to Induce Formation of the Virological Synapse.
- DOI:
10.1021/acsnano.5b00415 - 发表时间:
2015 - 期刊:
- 影响因子:17.1
- 作者:
Yu, Xinwei;Xu, Fangda;Ramirez, Nora-Guadalupe P.;Kijewski, Suzanne D. G.;Akiyama, Hisashi;Gummuluru, Suryaram;Reinhard, Bjoern M. - 通讯作者:
Reinhard, Bjoern M.
The Genetic Associations and Epistatic Effects of the CCR5 Promoter and CCR2-V64I Polymorphisms on Susceptibility to HIV-1 Infection in a Northern Han Chinese Population
CCR5启动子和CCR2-V64I多态性与北方汉族人群HIV-1感染易感性的遗传关联和上位效应
- DOI:
- 发表时间:
2012 - 期刊:
- 影响因子:1.4
- 作者:
Wang, Wei;Sheng, Aijuan;Wang, Youxin;Zhang, Ling;Wu, Jingjing;Song, Manshu;He, Yan;Yu, Xinwei;Zhao, Feifei - 通讯作者:
Zhao, Feifei
Oxidative Stress Responses and Gene Transcription of Mice under Chronic-Exposure to 2,6-Dichlorobenzoquinone.
- DOI:
10.3390/ijerph192113801 - 发表时间:
2022-10-24 - 期刊:
- 影响因子:0
- 作者:
Wu, Wenjing;Liu, Yingying;Li, Chunze;Zhuo, Fangyu;Xu, Zexiong;Hong, Huachang;Sun, Hongjie;Huang, Xianfeng;Yu, Xinwei - 通讯作者:
Yu, Xinwei
Spatial heterogeneity of urban-rural integration and its influencing factors in Shandong province of China.
- DOI:
10.1038/s41598-022-18424-0 - 发表时间:
2022-08-22 - 期刊:
- 影响因子:4.6
- 作者:
Shan, Baoyan;Zhang, Qiao;Ren, Qixin;Yu, Xinwei;Chen, Yanqiu - 通讯作者:
Chen, Yanqiu
Yu, Xinwei的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Yu, Xinwei', 18)}}的其他基金
Existence, Uniqueness, and Regularity for Equations in Mathematical Fluid Mechanics
数学流体力学方程的存在性、唯一性和正则性
- 批准号:
RGPIN-2019-05410 - 财政年份:2022
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Existence, Uniqueness, and Regularity for Equations in Mathematical Fluid Mechanics
数学流体力学方程的存在性、唯一性和正则性
- 批准号:
RGPIN-2019-05410 - 财政年份:2021
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Existence, Uniqueness, and Regularity for Equations in Mathematical Fluid Mechanics
数学流体力学方程的存在性、唯一性和正则性
- 批准号:
RGPIN-2019-05410 - 财政年份:2020
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Existence, Uniqueness, and Regularity for Equations in Mathematical Fluid Mechanics
数学流体力学方程的存在性、唯一性和正则性
- 批准号:
RGPIN-2019-05410 - 财政年份:2019
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2018
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2017
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2015
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2014
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
3D incompressible Euler equations: finite time singularities and Onsager's conjecture
3D 不可压缩欧拉方程:有限时间奇点和 Onsager 猜想
- 批准号:
371946-2009 - 财政年份:2013
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
3D incompressible Euler equations: finite time singularities and Onsager's conjecture
3D 不可压缩欧拉方程:有限时间奇点和 Onsager 猜想
- 批准号:
371946-2009 - 财政年份:2012
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
相似海外基金
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2018
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2017
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2015
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Regularity Problems in Mathematical Fluid Mechanics
数学流体力学中的正则性问题
- 批准号:
RGPIN-2014-06461 - 财政年份:2014
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Mathematical Sciences: Regularity and Singularity in Geometric Variational and Flow Problems
数学科学:几何变分和流问题中的正则性和奇异性
- 批准号:
9504456 - 财政年份:1995
- 资助金额:
$ 1.31万 - 项目类别:
Continuing Grant
Mathematical Sciences: Regularity Problems in Nonlinear Potential Theory and Quasiregular Mappings
数学科学:非线性势论和拟正则映射中的正则问题
- 批准号:
9208296 - 财政年份:1992
- 资助金额:
$ 1.31万 - 项目类别:
Standard Grant
Mathematical Sciences: Regularity Problems for Variational Integrals and Quasiregular Mappings
数学科学:变分积分和拟正则映射的正则问题
- 批准号:
9007946 - 财政年份:1990
- 资助金额:
$ 1.31万 - 项目类别:
Standard Grant
Mathematical Sciences: Regularity and Singularity in Constrained Variational Problems
数学科学:约束变分问题中的正则性和奇异性
- 批准号:
8914806 - 财政年份:1989
- 资助金额:
$ 1.31万 - 项目类别:
Continuing grant
Mathematical Sciences: Topics On Regularity Theory and Free Boundary Problems
数学科学:正则性理论和自由边界问题专题
- 批准号:
8802883 - 财政年份:1988
- 资助金额:
$ 1.31万 - 项目类别:
Continuing Grant
Mathematical Sciences: Regularity Theory for Certain Nonlinear Elliptic Equations and Related Variational Problems Involving Derivatives of Rearrangement of Solutions
数学科学:某些非线性椭圆方程和涉及解重排导数的相关变分问题的正则理论
- 批准号:
8896120 - 财政年份:1987
- 资助金额:
$ 1.31万 - 项目类别:
Standard Grant