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On singular vortex patches, II: Long-time dynamics

  • Published:2020-07-08 Issue:9 Volume:373 Page:6757-6775
  • ISSN:0002-9947
  • Container-title:Transactions of the American Mathematical Society
  • language:en
  • Short-container-title:Trans. Amer. Math. Soc.

Author:

Elgindi Tarek,Jeong In-Jee

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.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference41 articles.

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2. Motions of vortex patches;Burbea, Jacob;Lett. Math. Phys.,1982

3. T. F. Buttke, The observation of singularities in the boundary of patches of constant vorticity, Phys. Fluids A 1 (1989), 1283–1285.

4. Asymptotic behaviour of vortex patches: a case of confinement;Caglioti, E.;Boll. Un. Mat. Ital. B (7),1996

5. Scattering theory: a possible approach to the homogenization problem for the Euler equations;Caglioti, E.;Rend. Mat. Appl. (7),1997

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