Frontiers in Mathematics Lecture Series

Date: September 11, 2017

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Diego Cordoba, Consejo Superior de Investigaciones Científicas, Madrid, Spain

Title: Graduate Lecture: Splash and splat singularities for incompressible fluid interfaces

Abstract: The evolution of an interface between two immiscible incompressible fluids can develop singularities in finite time. In particular those contour dynamics that are given by basic fluid mechanics systems: Euler´s equations, Darcy´s law and the Quasi-geostrophic equation. These give rise to problems such as water wave, Muskat, and the evolution of sharp fronts of temperature. In this lecture we will present the main ideas and arguments of the formation in finite time of splash and splat singularities. A splash singularity is when the interfaceremains smooth but self-intersects at a point and a splat singularity is when it self-intersects along an arc.