Non-existence and strong ill-posedness in $C^{k,\beta }$ for the generalized Surface Quasi-geostrophic equation

Diego Córdoba, Luis Martínez-Zoroa

We consider solutions to the generalized Surface Quasi-geostrophic equation ($\gamma$-SQG) when the velocity is more singular than the active scalar function (i.e. $\gamma \in (0,1)$). In this…