Workshop on Geometry and Analysis of Fluid Flows

流体流动几何与分析研讨会

• 批准号: 2230558
• 负责人: Marcelo Disconzi
• 金额: $ 4.64万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-15 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2230558&HistoricalAwards=false
• 关键词: Workshop; Geometry; Analysis; Fluid; Flows

This award supports participation in the "Workshop on the Geometry and Analysis of Fluid Flows" hosted at Stony Brook University during the week of January 16-20, 2023. The fundamental equations of fluid mechanics describe many natural phenomena, including the motion of air in weather modeling, the lift of an airplane, mixing of fluids with applications in industry, flow of liquids through pipes, generation of electricity through wind and water, and the flow of blood through the body. The full equations are too difficult to solve explicitly or even by computer, hence mathematical attention focuses on properties of the equations. Such properties include whether solutions for given initial conditions exist for a long time or break down in finite time; whether solutions are stable and can be predicted with small errors, or fundamentally unstable and unpredictable; and the validity of simplifying approximations used to make the equations more manageable. These questions are difficult and longstanding. For instance, the question of long-time existence for the idealized three-dimensional fluid equations has remained open for well over a century. Both analysis and geometry have been used to study such questions, and the primary goal of this conference is to bring together senior and junior researchers with expertise in these two areas to share perspectives, techniques, and results, and to train the new generation of mathematicians.The workshop will feature a mathematically diverse group of speakers whose expertise spans multiple relevant areas. Topics to be discussed at the workshop include free boundary problems in fluid dynamics, the geometry of infinite-dimensional groups, singular limits in fluid flows, well-posedness and regularity of fluid equations, and differential geometric methods in mathematics and physics. Some of the talks will focus on issues of global existence for the three-dimensional Euler and Navier-Stokes equations; the limiting behavior as viscosity, compressibility, or surface tension approaches zero; the infinite-dimensional geometry describing fluid flows as geodesics; and well-posedness results for free boundary problems. The organizers are currently writing a textbook on geometric and analytic methods in fluid mechanics; a draft of this book will be distributed during the workshop for the benefit of participants.https://my.vanderbilt.edu/geoanalysisffThis 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.

This award supports participation in the "Workshop on the Geometry and Analysis of Fluid Flows" hosted at Stony Brook University during the week of January 16-20, 2023. The fundamental equations of fluid mechanics describe many natural phenomena, including the motion of air in weather modeling, the lift of an airplane, mixing of fluids with applications in industry, flow of liquids through pipes, generation of electricity through wind and water, and the flow of blood through the 身体。整个方程式很难明确或通过计算机求解，因此数学关注的重点是方程的属性。这些属性包括长期存在的给定初始条件的解决方案还是在有限的时间内分解；解决方案是稳定的，并且可以通过小错误或根本上不稳定和不可预测来预测；以及简化用于使方程式更易于管理的近似值的有效性。这些问题很困难且长期存在。例如，理想化的三维流体方程式的长期存在问题一直在一个多世纪以上。分析和几何形状均已用于研究此类问题，这次会议的主要目的是将这两个领域的高级和初级研究人员汇集在一起​​，以分享观点，技术和结果，并培训新一代数学家。该研讨会将以数学上多样化的代言人为特色。在研讨会上要讨论的主题包括流体动力学中的自由边界问题，无限维组的几何形状，流体流中的奇异限制，流体方程的良好性和规律性以及数学和物理学的差异几何方法。一些谈判将重点介绍三维Euler和Navier-Stokes方程的全球存在问题；限制行为作为粘度，可压缩性或表面张力接近零；将流体流动为大地学的无限维几何形状。自由边界问题的适应性结果。组织者目前正在撰写有关流体力学中几何和分析方法的教科书；本书的草稿将在研讨会期间分发。