Title: Local Existence and Blow-Up For SQG Patches

Date: 12/06/2019

Time: 4:10 PM - 5:00 PM

Place: A203 Wells Hall

The two-dimensional surface quasi-geostrophic (SQG) equation is a model for atmospheric or oceanic flows and has strong structural similarity with the 3D Euler equation. Interpolating be-tween the 2D Euler equation and the 2D SQG equation, one obtains the one-parameter $0\leq\alpha\leq1$ family of generalized SQG (gSQG) equations. The problem of wellposedness or finite time singularity for the gSQG equations is considered, with the aim of resolving this question for the 2D SQG equation $\alpha=1$. Recently, patch solutions that become singular in finite time have been constructed for a subfamily of the gSQG equations in the half-plane setting. We discuss this result and also discuss a blow-up criterion of lower regularity than suggested by numerics.