Conference: Recent Advances in Mathematical Fluid Dynamics

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，紧接着是5月20日至24日的会议。数学流体动力学的一个主要挑战是研究基本数学模型的可行性，如欧拉方程和纳维-斯托克斯方程，在相当长的时间间隔内。另一个主要挑战是确定模型对湍流现象和流体长期流动行为的描述。这些看似不相关的研究领域由一系列核心原则和技术联系在一起。暑期学校和会议的主要目标之一是汇集流体方程分析的领先专家，探索这些联系并绘制未来的行动路线，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。奖金将用于支付参与者的旅行和当地费用，并强调对学生、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、长时间和统计行为。近年来，流体流动的偏微分方程分析和相关方程在上述所有方面都取得了许多重要进展。在弱光滑解的适位性和短时行为的研究方面已经取得了许多突破。引入了强大的技术来研究与基本方程和相关模型的适定性有关的许多问题。在解的长期行为和统计性质的研究方面也取得了惊人的进展，其中发现了新的和看似一般的松弛机制。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，并为他们提供了一个促进合作和健康交流思想的场所。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

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.