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arXiv · 2206.05861

Existence of Solutions to Fluid Equations in H\"{o}lder and Uniformly Local Sobolev Spaces

David M. Ambrose·Elaine Cozzi·Daniel Erickson·James P. Kelliher
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Abstract

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.

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David M. Ambrose, Elaine Cozzi, Daniel Erickson, James P. Kelliher. 2022-06-13. Existence of Solutions to Fluid Equations in H\"{o}lder and Uniformly Local Sobolev Spaces. https://arxiv.org/abs/2206.05861

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