CAREER: Singularities in fluids

职业：流体中的奇点

• 批准号: 2145716
• 负责人: Tristan Buckmaster
• 金额: $ 45万
• 依托单位: Princeton University
• 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 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2145716&HistoricalAwards=false
• 关键词: CAREER; Singularities; fluids

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.

无数的流体动力现象是用奇异性来描述的，其中最著名的是，由于空气或水的介质中的干扰，比局部声音速度更快地形成了冲击波。该项目的目的是为围绕流体奇异性研究的研究和教学活动创建一个广泛的计划。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来设计适合本科生的项目。该项目还将旨在生产一本有关可压缩流体冲击波的基础研究生教科书。研究组件分为三个项目：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进行自相似的爆炸。在PI及其合作者的先前工作的基础上，第一个项目的目的是为多维压缩欧拉方程提供第一个完整的冲击波形成和开发的描述。第二个项目涉及进一步开发针对等性压缩流的自相似溶解解决方案的先前工作，以研究新型奇点的可能性。第三个项目涉及利用知情的神经网络来搜索流体中的新形式的奇异性，其存在将通过计算机辅助证明进行严格，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审查标准来通过评估来支持的。