Daniel Peralta-Salas (Institute of Mathematical Sciences): Steady incompressible fluid flows: a zoo of complexity

The dynamics of an incompressible and inviscid fluid flow is described by the Euler equations, a system of nonlinear PDEs that was introduced by Leonhard Euler more than 250 years ago. In spite of the many efforts to understand the solutions of these equations, several fundamental questions remain widely open. In this talk I will focus on the study of steady (or stationary) fluid flows, i.e., time independent solutions to the Euler equations. I will survey recent results showing the astonishing complexity of these solutions from the topological, dynamical and computational viewpoints.