Small scale creation in ideal fluid

PDE Seminar
Tuesday, September 26, 2017 - 15:05
1 hour (actually 50 minutes)
Skiles 006
Duke University
I will review recent results on small scale creation in solutions of the Euler equation. A numerical simulation due to Hou and Luo suggests a new scenario for finite time blow up in three dimensions. A similar geometry in two dimensions leads to examples with very fast, double exponential in time growth in the gradient of vorticity. Such growth is know to be sharp due to upper bounds going back to 1930s. If I have time, I will also discuss several models that have been proposed to help understand the three-dimensional case.