Summer School in mathematics 2023 - New trends in mathematical fluid dynamics

This summer school focuses on the most modern aspects of the mathematical analysis of Partial Differential Equations in fluid mechanics. Its goal is a unified presentation of recently developed mathematical tools for the study of three fundamental problems in fluid dynamics: the behavior of anisotropic flows (boundary layers, shallow water flows), the dynamics of vortex structures, and the evolution of floating structures on waves. Even if the physical situations are very different, these problems share many characteristics in terms of mathematical analysis. Their common point is that they are described by singular solutions of the Euler or Navier-Stokes equations. The term "singular" evokes here : - either a lack of regularity, which manifests itself for vorticity filaments (described by Dirac masses along curves), or at the contact line between a fluid and a floating structure ; - or a singular dependence of the solution on a parameter, typically the Reynolds number (as in boundary layers).