Applied Mathematics Colloquium

Abstract: In this talk we will introduce the Navier-Stokes equations, beginning with the contributions of Jean Leray in 1934.  We will then discuss the historically important class of self similar solutions and recent results concerning their existence.  These solutions go back to Leray's own work; he identified them as possible candidates for a finite time singularity.  They remain relevant today.  For example, they are thought to be good candidates for discovering non-uniqueness.