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

Zachary Radke

doi:10.48550/arxiv.2507.09058

July 11, 2025Open Access

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

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Key Points

Non-decaying solutions exist for the generalized surface quasi-geostrophic equations, emphasizing stability in certain spaces.
The study proves uniqueness in Hölder-Zygmund spaces $C^r(ℝ^2)$ for $r>1$ and Sobolev spaces $H_{ul}^s(ℝ^2)$ for $s>2$.
Short-time existence is confirmed, indicating the solutions are reliable for initial timeframes.
This research expands on mathematical understanding of dynamics governed by the generalized quasi-geostrophic equations.

Implication

We establish existence and uniqueness of non-decaying solutions in Hölder-Zygmund and Sobolev spaces.

Abstract

We establish the short-time existence and uniqueness of non-decaying solutions to the generalized Surface Quasi-Geostrophic equations in Hölder-Zygmund spaces Cʳ(R²) for $r>1$ and uniformly local Sobolev spaces Hᵤₗˢ(R²) for $s>2$.

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Cite This Study

Zachary Radke (2025) studied this question.

synapsesocial.com/papers/68de5d9c83cbc991d0a204b4 https://doi.org/10.48550/arxiv.2507.09058

View Full Paper

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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