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: 1945669
• 负责人: Tarek Elgindi
• 金额: $ 44.9万
• 依托单位: University of California-San Diego
• 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 2020-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1945669&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.

流体动力学的应用范围涵盖生物过程、空气动力学和气象学的研究，仍然是经典和现代物理学最重要的领域之一。尽管流体对几乎所有生命都很重要，但人们对如何预测一般环境中的流体运动知之甚少。该项目的目标是增进我们对有关流体流动的一些基本问题的了解：经典物理定律是否足以提供所有情况下流体流动的完整图像？更准确地说，是否存在导致流体运动的经典定律失效的极端事件？如果是这样，有没有办法修改经典定律，以在这种情况下给出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（欧拉方程和纳维-斯托克斯方程）的全局可解性问题相关。这项工作的重点将是欧拉方程的奇点形成问题。我们将分析最近构造的奇点形成示例的稳定性，并研究这些示例可以扩展到何种程度以给出更常规解决方案的奇点形成。与此同时，我们将考虑增强耗散问题，并研究无粘性问题中可能的奇异行为对粘性问题中快速耗散的影响。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。