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arXiv · 2504.17199

Horizontally periodic generalized surface quasigeostrophic patches and layers

David M. Ambrose·Fazel Hadadifard·James P. Kelliher
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Abstract

We study solutions to the $\alpha$-SQG equations, which interpolate between the incompressible Euler and surface quasi-geostrophic equations. We extend prior results on existence of bounded patches, proving propagation of $H^k$-regularity of the patch boundary, $k \ge 3$, for finite time for patches that are periodic in one spatial dimension. Such periodic patches also encompass layers, or two-sided fronts. As the authors have treated the Euler case in prior work, we now primarily focus on the range of $\alpha$ for which $\alpha$-SQG lies strictly between the Euler and SQG equations.

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David M. Ambrose, Fazel Hadadifard, James P. Kelliher. 2025-04-24. Horizontally periodic generalized surface quasigeostrophic patches and layers. https://arxiv.org/abs/2504.17199

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