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An improved
regularity criterion and absence of splash-like singularities
for g-SQG patches
Junekey Jeon and Andrej Zlatoš |
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Vol. 17 (2024), No. 3, 1005–1018
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Abstract |
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We prove that splash-like singularities cannot occur for sufficiently regular patch solutions to the generalized surface quasi-geostrophic equation on the plane or half-plane with parameter . This includes potential touches of more than two patch boundary segments in the same location, an eventuality that has not been excluded previously and presents nontrivial complications (in fact, if we do a priori exclude it, then our results extend to all ). As a corollary, we obtain an improved global regularity criterion for patch solutions when , namely that finite time singularities cannot occur while the norms of patch boundaries remain bounded. |
Keywords
generalized SQG equation, patch solutions, splash
singularity
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Mathematical Subject Classification
Primary: 35Q35
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Milestones
Received: 5 December 2021
Revised: 15 May 2022
Accepted: 11 August 2022
Published: 24 April 2024
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Authors |
| Junekey Jeon | |
| Department of Mathematics University of California San Diego La Jolla, CA United States |
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| Andrej Zlatoš | |
| Department of Mathematics University of California San Diego La Jolla, CA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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