Small scale creation in inviscid fluids

Alexander Kiselev (Rice University)

The problem of global regularity vs finite time blow up for the classical 3D equations of fluid mechanics is one of the well known open problems of applied analysis. Recently, a new scenario for finite time blow up of solutions to 3D Euler equation has been proposed by Hou and Luo based on extensive numerical simulation.

We will describe some recent analytic developments stimulated by Hou and Luo work. We will begin with the two-dimensional Euler equation, where an example leading to the double exponential growth for all times in the vorticity gradient has been constructed. We will then discuss some models that help bridge the gap between two and three dimensions, and may help to gain insight into the nature of possible blow up in 3D Euler.