# Non existence and strong ill-posedness in $C^k$ and Sobolev spaces for SQG

TURW02 - Rigorous analysis of incompressible fluid models and turbulence

We construct solutions in $\mathds{R}2$ with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in $Ck$($k\geq 2$) but that are not in $C$ for $t>0$.  We prove a similar result also for $H{s}$ in the range $s\in(\frac32,2)$.  Moreover, we prove similar results in Holder spaces for a familty of active scalars more singular than SQG .  This is a joint work with Luis Martinez-Zoroa.

This talk is part of the Isaac Newton Institute Seminar Series series.