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

基本信息

  • 批准号:
    1614918
  • 负责人:
  • 金额:
    $ 40.73万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2016
  • 资助国家:
    美国
  • 起止时间:
    2016-09-01 至 2020-08-31
  • 项目状态:
    已结题

项目摘要

The main part of the project concerns the study of dramatic behaviors in fluid mechanics known as shocks. A typical example, in oceanography, is the propagation of a tsunami. Understanding flows with shocks is of particular importance for engineering and industry. The investigator studies the stability of such structures using state of the art mathematical tools. The project focuses on these specific goals: (1) Advance the knowledge of physical systems that are of fundamental importance in engineering, meteorology, medicine, or natural disasters, such as flooding and tsunamis; (2) Develop powerful mathematical tools, based on the theory of nonlinear partial differential equations, that can be used to study these systems. Graduate students are involved in the work of the project, which provides good opportunities for training junior researchers in mathematical analysis and physical modeling.The investigator studies the stability of discontinuous solutions in compressible fluid mechanics, known as shocks. They are linked to intriguing behaviors of fluids, especially in supersonic flows. This project advances the understanding of these phenomena. A special emphasis is on the study of asymptotic limits from viscous models such as compressible Navier-Stokes equations, or from kinetic models. These problems involve the study of layers subject to large perturbations. The investigator also studies the existence and properties of solutions to related models, such as compressible Navier-Stokes equations with degenerated viscosities, or nonlinear nonhomogeneous kinetic equations. For this purpose, the investigator uses and develops deep analysis tools, such as the De Giorgi method and the relative entropy method.
该项目的主要部分涉及流体力学中的戏剧性行为的研究,称为冲击。 在海洋学中,一个典型的例子是海啸的传播。 了解具有冲击的流动对于工程和工业特别重要。 研究人员使用最先进的数学工具研究这种结构的稳定性。 该项目侧重于这些具体目标:(1)推进对工程,气象,医学或自然灾害(如洪水和海啸)具有根本重要性的物理系统的知识;(2)开发基于非线性偏微分方程理论的强大数学工具,可用于研究这些系统。研究生参与了该项目的工作,该项目为培训数学分析和物理建模方面的初级研究人员提供了良好的机会。研究员研究可压缩流体力学中不连续解的稳定性,称为冲击。 它们与流体的有趣行为有关,特别是在超音速流动中。 该项目促进了对这些现象的理解。 一个特别强调的是从粘性模型,如可压缩Navier-Stokes方程,或从动力学模型的渐近极限的研究。 这些问题涉及对受到大扰动的层的研究。 研究人员还研究了相关模型的解的存在性和性质,例如具有退化粘度的可压缩Navier-Stokes方程或非线性非齐次动力学方程。 为此,研究人员使用并开发了深入的分析工具,如De Giorgi方法和相对熵方法。

项目成果

期刊论文数量(17)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Hölder Regularity up to the Boundary for Critical SQG on Bounded Domains
Hölder 正则性达到有界域上关键 SQG 的边界
De Giorgi techniques applied to Hamilton–Jacobi equations with unbounded right-hand side
De Giorgi 技术应用于右侧无界的 Hamilton-Jacobi 方程
Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
  • DOI:
    10.1142/s0218202520500104
  • 发表时间:
    2019-04
  • 期刊:
  • 影响因子:
    3.5
  • 作者:
    Kyudong Choi;Moon-Jin Kang;Young-Sam Kwon;A. Vasseur
  • 通讯作者:
    Kyudong Choi;Moon-Jin Kang;Young-Sam Kwon;A. Vasseur
On uniqueness of solutions to conservation laws verifying a single entropy condition
验证单熵条件的守恒定律解的唯一性
Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system
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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:
    $ 40.73万
  • 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:
    $ 40.73万
  • 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:
    $ 40.73万
  • 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:
    $ 40.73万
  • 项目类别:
    Continuing Grant
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
  • 财政年份:
    2009
  • 资助金额:
    $ 40.73万
  • 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:
    $ 40.73万
  • 项目类别:
    Standard Grant

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