Existence of Solutions to Fluid Equations in Hölder and Uniformly Local Sobolev Spaces

David M. Ambrose, Elaine Cozzi, Daniel Erickson +1

We establish short-time existence of solutions to the surface quasi-geostrophic equation in both the Hölder spaces $C^r({\mathbb{R}}^2)$ for $r>1$ and the uniformly local Sobolev spa…