Existence of Non-Decaying Solutions to the Generalized Surface Quasi-Geostrophic Equations

We establish the short-time existence and uniqueness of non-decaying solutions to the generalized Surface Quasi-Geostrophic equations in Hölder-Zygmund spaces $C^r({\mathbb{R}}^2)$ for $r>1$ and uniformly local Sobolev spaces $H_{ul}^s({\mathbb{R}}^2)$ for $s>2$.