  We establish short-time existence of solutions to the surface
quasi-geostrophic equation in both the H\"{o}lder spaces $C^r(\mathbb{R}^2)$
for $r>1$ and the uniformly local Sobolev spaces $H^s_{ul}(\mathbb{R}^2)$ for
$s\geq 3$. Using methods similar to those for the surface quasi-geostrophic
equation, we also obtain short-time existence for the three-dimensional Euler
equations in uniformly local Sobolev spaces.
