On well/ill-posedness for the generalized surface quasi-geostrophic equations in Hölder spaces

Young-Pil Choi, Jinwook Jung, Junha Kim

We establish the well/ill-posedness theories for the inviscid $\alpha$-surface quasi-geostrophic ($\alpha$-SQG) equations in Hölder spaces, where $\alpha =0$ and $\alpha =1$ correspond to the two-dime…