Hamiltonian partial differential equations and dynamical systems, and their applications

哈密​​顿偏微分方程和动力系统及其应用

基本信息

  • 批准号:
    RGPIN-2016-05473
  • 负责人:
  • 金额:
    $ 3.35万
  • 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

项目摘要

My research program involves the analysis of solutions of partial differential equations (PDEs) that describe wave evolution in a broad spectrum of physical phenomena. I am working on problems of ocean wave dynamics, techniques of Hamiltonian mechanics and their applications to vortex dynamics, nonlinear Schrodinger equations including ones relevant to photonics, and many other problems in nonlinear waves. My research mostly involves theoretical analysis, contributing to the understanding of PDEs. However in the past it has had an impact on other disciplines, where advances lend themselves to more efficient numerical simulations or to a deeper conceptual understanding of experiments. And I often collaborate with physical scientists on projects in areas having to do with wave phenomena. This proposal is for research on the properties of solutions of specific PDEs that arise in the physical sciences, which describe wave phenomena such as free surface water waves, nonlinear optics, and continuum mechanics. This includes dispersive evolution equations such as the nonlinear Schrodinger and Klein - Gordon equations, vortex filament evolution for the Euler equations, and problems of water waves. I also plan to continue my prior analysis of the incompressible Navier - Stokes equations. This program has three principal objectives: (1) To address Hamiltonian PDEs from the point of view of a phase space analysis, extending the refined analytic techniques of Hamiltonian systems, such as KAM theory, normal forms, and Nekhoroshev stability, to the dynamics of PDEs in the appropriate infinite dimensional setting in which they are naturally posed. (2) To study free surface water waves in several settings, and to use their property of a Hamiltonian PDE to describe nonlinear interactions, solitary wave collisions, and asymptotic scaling regimes such as using homogenization techniques to describe waves over a variable bathymetry. (3) To consider aspects of regularity theory for the Navier - Stokes equations, including the ramifications of upper bounds on spectral behavior, and the recent microlocal lower bounds on the singular set. I always involve postdoctoral fellows and graduate students in my research projects. In addition, I am intending to address problems that have a potential value to other areas of science, and I plan to continue to seek out interesting collaborations with non-mathematician physical scientists, as I have successfully pursued in the past.
我的研究项目包括分析偏微分方程(PDEs)的解,这些方程描述了在广泛的物理现象中波动的演变。我的工作是海浪动力学问题,哈密顿力学技术及其在涡旋动力学中的应用,非线性薛定谔方程,包括与光子学相关的方程,以及非线性波中的许多其他问题。我的研究主要涉及理论分析,

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 }}

Craig, Walter其他文献

Global Wellposedness for the 3D Inhomogeneous Incompressible Navier–Stokes Equations
3D 非齐次不可压缩纳维斯托克斯方程的全局适定性
Bounds on Kolmogorov spectra for the Navier-Stokes equations
  • DOI:
    10.1016/j.physd.2011.10.013
  • 发表时间:
    2012-02-15
  • 期刊:
  • 影响因子:
    4
  • 作者:
    Biryuk, Andrei;Craig, Walter
  • 通讯作者:
    Craig, Walter

Craig, Walter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('Craig, Walter', 18)}}的其他基金

Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Analysis and its Applications
数学分析及其应用
  • 批准号:
    1000230412-2014
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs
Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical Analysis and its Applications
数学分析及其应用
  • 批准号:
    1000230412-2014
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs
Mathematical Analysis and its Applications
数学分析及其应用
  • 批准号:
    1000230412-2014
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs
Mathematical Analysis and its Applications
数学分析及其应用
  • 批准号:
    1230412-2014
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs
Partial differential equations, Hamiltonian dynamical systems, and their applications
偏微分方程、哈密顿动力系统及其应用
  • 批准号:
    238452-2011
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
The Institute Innovation Platform
研究院创新平台
  • 批准号:
    468798-2014
  • 财政年份:
    2014
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Partnerships Innovation Platform
Mathematical Analysis and Its Applications
数学分析及其应用
  • 批准号:
    1000204423-2007
  • 财政年份:
    2014
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs

相似国自然基金

Graphon mean field games with partial observation and application to failure detection in distributed systems
  • 批准号:
  • 批准年份:
    2025
  • 资助金额:
    0.0 万元
  • 项目类别:
    省市级项目
硝态氮氨化菌群富集及其与部分反硝化协同的机制研究
  • 批准号:
    51808045
  • 批准年份:
    2018
  • 资助金额:
    26.0 万元
  • 项目类别:
    青年科学基金项目
Partial EIV 模型参数估计理论及其在测量数据处理中的应用研究
  • 批准号:
    41664001
  • 批准年份:
    2016
  • 资助金额:
    40.0 万元
  • 项目类别:
    地区科学基金项目
Partial Spread Bent函数与Bent-Negabent函数的构造及密码学性质研究
  • 批准号:
    61402377
  • 批准年份:
    2014
  • 资助金额:
    25.0 万元
  • 项目类别:
    青年科学基金项目
图的l1-嵌入性以及partial立方图和多重median图的刻画
  • 批准号:
    11261019
  • 批准年份:
    2012
  • 资助金额:
    45.0 万元
  • 项目类别:
    地区科学基金项目
微分动力系统的测度和熵
  • 批准号:
    11101447
  • 批准年份:
    2011
  • 资助金额:
    22.0 万元
  • 项目类别:
    青年科学基金项目
部分双曲系统的遍历性研究
  • 批准号:
    11001284
  • 批准年份:
    2010
  • 资助金额:
    16.0 万元
  • 项目类别:
    青年科学基金项目
低温绝缘材料局部放电特性与电老化机理的研究
  • 批准号:
    50577038
  • 批准年份:
    2005
  • 资助金额:
    27.0 万元
  • 项目类别:
    面上项目

相似海外基金

(Semi)algebraic Geometry in Schrödinger Operators and Nonlinear Hamiltonian Partial Differential Equations
薛定谔算子和非线性哈密顿偏微分方程中的(半)代数几何
  • 批准号:
    2246031
  • 财政年份:
    2023
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Standard Grant
Some Dynamical Questions in Hamiltonian Partial Differential Equations
哈密​​顿偏微分方程中的一些动力学问题
  • 批准号:
    2007457
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Standard Grant
Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Hamiltonian partial differential equations and dynamical systems, and their applications
哈密​​顿偏微分方程和动力系统及其应用
  • 批准号:
    RGPIN-2016-05473
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Defect dynamics in nonlinear Hamiltonian partial differential equations
非线性哈密顿偏微分方程中的缺陷动力学
  • 批准号:
    261955-2013
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Hamiltonian Partial Differential Equations
哈密​​顿偏微分方程
  • 批准号:
    250233-2012
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Defect dynamics in nonlinear Hamiltonian partial differential equations
非线性哈密顿偏微分方程中的缺陷动力学
  • 批准号:
    261955-2013
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Defect dynamics in nonlinear Hamiltonian partial differential equations
非线性哈密顿偏微分方程中的缺陷动力学
  • 批准号:
    261955-2013
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Hamiltonian Partial Differential Equations
哈密​​顿偏微分方程
  • 批准号:
    250233-2012
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了