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Bibliographic Details
Main Authors: Ambrose, David M., Hadadifard, Fazel, Kelliher, James P.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.17199
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Table of Contents:
  • We study solutions to the $α$-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 $α$ for which $α$-SQG lies strictly between the Euler and SQG equations.