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Journal article
CONTOUR DYNAMICS AND GLOBAL REGULARITY FOR PERIODIC VORTEX PATCHES AND LAYERS
SIAM journal on mathematical analysis, v 56(2), pp 2286-2311
01 Jan 2024
Abstract
We study vortex patches for the two-dimensional incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We instead consider the horizontally periodic setting. This includes both the case of a periodic array of bounded vortex patches and the case of vertically bounded vortex layers. We develop the contour dynamics equation for the boundary of the patch in this horizontally periodic setting and demonstrate global C1,\varepsilon regularity of this patch boundary. In the process of formulating the problem, we consider different notions of periodic solutions of the two-dimensional incompressible Euler equations and demonstrate equivalence of these.
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Details
- Title
- CONTOUR DYNAMICS AND GLOBAL REGULARITY FOR PERIODIC VORTEX PATCHES AND LAYERS
- Creators
- David M. Ambrose - Drexel UniversityFazel Hadadifard - University of California, RiversideJames P. Kelliher - University of California, Riverside
- Publication Details
- SIAM journal on mathematical analysis, v 56(2), pp 2286-2311
- Publisher
- Siam Publications
- Number of pages
- 26
- Grant note
- DMS-1907684; DMS-2307638 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001186482800001
- Scopus ID
- 2-s2.0-85188247596
- Other Identifier
- 991021867244004721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied