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

Abstract

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