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

Zachary Radke

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

Analysis of PDEs 2025-07-15 v1

Authors: Zachary Radke

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 $s>2$ .

Keywords

Surface Quasi-Geostrophic equations non-decaying solutions Holder-Zygmund spaces Sobolev spaces existence and uniqueness

Cite

@article{arxiv.2507.09058,
  title  = {Existence of Non-Decaying Solutions to the Generalized Surface Quasi-Geostrophic Equations},
  author = {Zachary Radke},
  journal= {arXiv preprint arXiv:2507.09058},
  year   = {2025}
}

Comments

30 pages

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