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Transactions of the American Mathematical Society

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On singular vortex patches, II: Long-time dynamics


Authors: Tarek M. Elgindi and In-Jee Jeong
Journal: Trans. Amer. Math. Soc. 373 (2020), 6757-6775
DOI: https://doi.org/10.1090/tran/8134
Published electronically: July 8, 2020
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Abstract | References | Additional Information

Abstract: In a companion paper [arXiv:1903.00833], we gave a detailed account of the well-posedness theory for singular vortex patches. Here, we discuss the long-time dynamics of some of the classes of vortex patches we showed to be globally well-posed in the above-mentioned paper. In particular, we give examples of time-periodic behavior, cusp formation in infinite time at an exponential rate, and spiral formation in infinite time.


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Additional Information

Tarek M. Elgindi
Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093
MR Author ID: 990694
Email: telgindi@ucsd.edu.

In-Jee Jeong
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 85 Hoegi-ro, Cheongnyangri-dong, Dongdaemun-gu, Seoul, South Korea
MR Author ID: 1055009
Email: ijeong@kias.re.kr

DOI: https://doi.org/10.1090/tran/8134
Received by editor(s): October 17, 2019
Received by editor(s) in revised form: February 12, 2020
Published electronically: July 8, 2020
Additional Notes: The first author was partially supported by grant number NSF DMS-1817134.
The second author was supported by a KIAS Individual Grant MG066202 at Korea Institute for Advanced Study, the Science Fellowship of POSCO TJ Park Foundation, and the National Research Foundation of Korea grant (No. 2019R1F1A1058486).
Article copyright: © Copyright 2020 American Mathematical Society