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CAREER: Singularities in fluids

职业：流体中的奇点

基本信息

批准号：
2243205
负责人：
Tristan Buckmaster
金额：
$ 45万
依托单位：
University of Maryland, College Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2027-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2243205&HistoricalAwards=false
关键词：
CAREER Singularities fluids

项目摘要

Innumerable hydrodynamical phenomena are described in terms of singularities, of which perhaps the most well-known is the formation of shock waves resulting from a disturbance in a medium such as air or water moving faster than the local speed of sound. The goal of this project is to create a broad program for both research and pedagogical activities centered around the study of singularities in fluids. The award will provide research opportunities and training for postdoctoral scholars and will leverage its research elements to design projects suitable for undergraduate students. The project will also aim at producing a foundational graduate textbook on shock waves in compressible fluids.The research component is split into three projects: formation and development of shock waves, radial implosions from smooth initial data, and self-similar blow-up via neural networks. Building on previous work of the PI and his collaborators, the aim of the first project will be to provide the first full description of shock wave formation and development for the multi-dimensional compressible Euler equations. The second project involves further developing prior work on self-similar imploding solutions for isentropic compressible flows to investigate the possibility of new types of singularities. The third project involves utilizing physically informed neural networks to search for new forms of singularities in fluid, whose existence will be made rigorous through the aid of computer assisted proofs.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.

非线性流体动力学现象是用奇点来描述的，其中最著名的可能是由于空气或水等介质中的扰动比当地声速更快而形成的冲击波。这个项目的目标是创建一个广泛的研究和教学活动围绕着研究流体中的奇点。该奖项将为博士后学者提供研究机会和培训，并将利用其研究元素设计适合本科生的项目。该项目还旨在编写一本关于可压缩流体中冲击波的基础研究生教科书。研究部分分为三个项目：冲击波的形成和发展，光滑初始数据的径向内爆，以及通过神经网络的自相似爆破。在PI及其合作者以前工作的基础上，第一个项目的目标是为多维可压缩欧拉方程提供冲击波形成和发展的第一个完整描述。第二个项目涉及进一步发展等熵可压缩流的自相似内爆解的先前工作，以研究新类型奇点的可能性。第三个项目涉及利用物理信息神经网络来寻找流体中的新形式奇点，其存在将通过计算机辅助证明的帮助进行严格验证。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。