Conference: Recent Advances in Mathematical Fluid Dynamics

会议：数学流体动力学的最新进展

• 批准号: 2247145
• 负责人: Tarek Elgindi
• 金额: $ 4.95万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-03-15 至 2024-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2247145&HistoricalAwards=false
• 关键词: Conference; Recent; Advances; Mathematical; Fluid

The conference and summer school "Recent Advances in Mathematical Fluid Dynamics" to be held at Duke University from May 16-24, 2023. The summer school will be from May 16-19, immediately followed by the conference from May 20-24. One major challenge in mathematical fluid dynamics is to study the viability of the basic mathematical models, like the Euler and Navier-Stokes equations, on reasonably long intervals of time. Another major challenge is to determine what the models have to say about turbulent phenomena and the behavior of fluid flows in the long-term. These seemingly unrelated areas of study are connected by a core of principles and techniques. One of the main goals of the summer school and conference is to bring together leading experts in the analysis of fluid equations to explore these connections and chart future a course of action, to provide junior researchers with the tools to enter these fields, and to bring the opportunity to disseminate and discuss the latest cutting-edge results in the field. The award funds will help defray travel and local expenses of the participants, emphasizing the support of a diverse group of students, postdocs, and junior researchers. The main questions that will be considered at this conference relate to the well-posedness and the long-time and statistical behavior of fluid equations and related physical models. In recent years, the PDE analysis of fluid flows and related equations has seen numerous important advances on all the above fronts. There have been numerous breakthroughs in the study of well-posedness and the short-time behavior of solutions, both weak and smooth. Powerful techniques have been introduced to study many problems related to well-posedness of the fundamental equations and related models. There have also been spectacular advances on the study of the long-time behavior and statistical properties of solutions, where new and seemingly generic relaxation mechanisms have been discovered. The conference we are organizing brings together experts from around the world to present recent advances in these areas of research and gives them a venue to foster collaboration and a healthy exchange of ideas. The conference website is https://sites.duke.edu/fluids/.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.

会议和暑期学校“数学流体动力学的最新进展”将于 2023 年 5 月 16 日至 24 日在杜克大学举行。暑期学校将于 5 月 16 日至 19 日举行，紧接着的会议将于 5 月 20 日至 24 日举行。数学流体动力学的一项主要挑战是研究基本数学模型（例如欧拉方程和纳维-斯托克斯方程）在相当长的时间间隔内的可行性。另一个主要挑战是确定模型对湍流现象和流体流动的长期行为有何看法。这些看似无关的研究领域通过核心原理和技术联系在一起。暑期学校和会议的主要目标之一是聚集流体方程分析领域的领先专家，探索这些联系并规划未来的行动方案，为初级研究人员提供进入这些领域的工具，并带来传播和讨论该领域最新前沿成果的机会。该奖项资金将帮助支付参与者的旅费和当地费用，强调来自不同群体的学生、博士后和初级研究人员的支持。 本次会议将考虑的主要问题涉及流体方程和相关物理模型的适定性以及长期统计行为。近年来，流体流动和相关方程的偏微分方程分析在上述所有领域都取得了许多重要进展。在弱解和光滑解的适定性和短时行为的研究方面已经取得了许多突破。强大的技术已被引入来研究与基本方程和相关模型的适定性相关的许多问题。对解的长期行为和统计特性的研究也取得了惊人的进展，发现了新的、看似通用的松弛机制。我们正在组织的会议汇集了来自世界各地的专家，介绍这些研究领域的最新进展，并为他们提供了促进合作和健康交流思想的场所。会议网站是 https://sites.duke.edu/fluids/。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。