Finite time singularity of a vortex patch model in the half plane
Finite time singularity of a vortex patch model in the half plane

Yao Yao , University of Wisconsin
Fine Hall 322
The question of global regularity vs. finite time blowup remains open for many fluid equations. In this talk, I will discuss an active scalar equation which is an interpolation between the 2D Euler equation and the surface quasigeostrophic equation. We study the patch dynamics for this equation in the halfplane, and prove that the solutions can develop a finitetime singularity. This is a joint work with A. Kiselev, L. Ryzhik and A. Zlatos.