Title: Finite time singularities for incompressible fluids

Abstract: The question of singularity formation in fluid dynamics remains one of  the most challenging open problems in mathematical physics. In this  talk, we present new results showing that solutions to 3D  hypodissipative Navier-Stokes equations with smooth initial data and an  external forcing that is integrable in C^{1+ϵ} can break down in finite  time. The dissipation in the equation amounts to 0.092 orders of  derivative, or (−∆)^{0.046}. Time permitting, I will discuss extensions  that allow for more dissipation and rougher forcing.