Preprint
Horizontally periodic generalized surface quasigeostrophic patches and layers
23 Apr 2025
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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Details
- Title
- Horizontally periodic generalized surface quasigeostrophic patches and layers
- Creators
- David M AmbroseFazel HadadifardJames P Kelliher
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022049009504721