The $\hat{I}\pm$-SQG patch problem is illposed in $C^{2,{\hat{I}}^2}$ and $W^{2,p}$

Alexander Kiselev, Xiaoyutao Luo

We consider the patch problem for the $\hat{I}\pm$-SQG system with the values $\hat{I}\pm =0$ and $\hat{I}\pm =\frac{1}{2}$ being the 2D Euler and the SQG equations respectively. It is well-known that the…