Conference: Recent Advances in Mathematical Fluid Dynamics

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.