CAREER:Formation of Small Scales and Dissipation in Incompressible Fluids

职业：不可压缩流体中小尺度的形成和耗散

• 批准号: 2043024
• 负责人: Tarek Elgindi
• 金额: $ 44.9万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2043024&HistoricalAwards=false
• 关键词: CAREER; Formation; Small; Scales; Dissipation

With applications ranging from the study of biological processes, aerodynamics, and meteorology, fluid dynamics remains one of the most important fields of classical and modern physics. Despite the importance of fluids to virtually all life, little is known about how to predict fluid motion in general settings. The goal of this project is to advance our knowledge of some of the fundamental questions regarding fluid flow: are the laws of classical physics sufficient to provide a complete picture of fluid flow in all scenarios? More precisely, are there extreme events in which the classical laws governing fluid motion break down? If so, is there a way to amend the classical laws to give effective models of fluid motion in such circumstances? This award also supports the involvement of a postdoctoral scholar and a graduate student in the research project. Mathematically, these questions relate to the question of the global solvability for the classical fluid equations: the Euler and Navier-Stokes equations. The focus of this work will be on the problem of singularity formation for the Euler equation. We will analyze the stability of recently constructed examples of singularity formation and study the extent to which these examples can be extended to give singularity formation for more regular solutions. In parallel, we will consider the problem of enhanced dissipation and study the effects of possible singular behavior in inviscid problems on rapid dissipation in viscous problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

随着对生物过程，空气动力学和气象学的研究的应用，流体动力学仍然是古典物理和现代物理学中最重要的领域之一。尽管流体对几乎所有生命都重要，但对于如何预测一般环境中的流体运动知之甚少。该项目的目的是提高我们对流体流动的一些基本问题的了解：在所有情况下，经典物理定律足以提供流体流动的完整图片？更确切地说，是否存在执行流体运动的经典法律破裂的极端事件？如果是这样，是否有一种方法可以修改经典法律，以在这种情况下提供有效的流体运动模型？该奖项还支持博士后学者和研究生参与研究项目。从数学上讲，这些问题与经典流体方程的全球可溶性问题有关：Euler和Navier-Stokes方程。这项工作的重点将放在欧拉方程的奇异性形成问题上。我们将分析最近构建的奇异性形成实例的稳定性，并研究可以扩展这些示例的程度，从而为更常规的解决方案提供奇异性形成。同时，我们将考虑增强耗散的问题，并研究粘性问题中可能的奇异行为对粘性问题快速耗散的影响。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估标准来评估的支持。

项目成果

Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

• DOI: 10.1007/s00205-023-01842-3
• 发表时间: 2020-07
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: Michele Coti Zelati;T. Elgindi;Klaus Widmayer

Finite-time singularity formation for an active scalar equation

主动标量方程的有限时间奇点形成

• DOI: 10.1088/1361-6544/ac0231
• 发表时间: 2021
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: Elgindi, Tarek;Ibrahim, Slim;Shen, Shengyi
• 通讯作者: Shen, Shengyi

Anomalous Dissipation in Passive Scalar Transport

• DOI: 10.1007/s00205-021-01736-2
• 发表时间: 2022-01-16
• 期刊: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
• 影响因子: 2.5
• 作者: Drivas, Theodore D.;Elgindi, Tarek M.;Jeong, In-Jee
• 通讯作者: Jeong, In-Jee

Growth of Sobolev norms and loss of regularity in transport equations

• DOI: 10.1098/rsta.2021.0024
• 发表时间: 2022-06-13
• 期刊: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
• 影响因子: 5
• 作者: Crippa, Gianluca;Elgindi, Tarek;Mazzucato, Anna L.
• 通讯作者: Mazzucato, Anna L.

On Singular Vortex Patches, I: Well-posedness Issues

• DOI: 10.1090/memo/1400
• 发表时间: 2019-03
• 期刊: Memoirs of the American Mathematical Society
• 影响因子: 1.9
• 作者: T. Elgindi;In-Jee Jeong