Seminars & Colloquia Calendar

In this talk I will review several concepts of classical and weak solutions for the incompressible Euler and Navier-Stokes equations. I will then motivate why it is reasonable to look for extensions of the usual concept of smooth solutions and give an overview of what is currently known about the generalized ones in terms of existence, uniqueness, and regularity. In particular I will outline how some techniques inspired by classical results in differential geometry have recently lead to the discovery of several patological behaviors for seemingly reasonable notions of solutions.