Despite a quarter of a century of history, the nature of solutions of the Euler equations remains an open problem. To date, it is not known if smooth initial conditions of the Euler equations with finite energy do or do not blow-up in finite time. I will review the approach initiated by Leray of self-similar blow-up solutions. Lastly, I will show that under some conditions an axisymmetric incompressible and inviscid flow presents a finite-time singularity. This singularity appears to be generic and robust for a wide number of finite energy initial conditions.
Speaker: Sergio Rica.
Full Professor, Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez.