Communications in Mathematical Physics

, Volume 152, Issue 1, pp 19–28 | Cite as

Global regularity for vortex patches

  • A. L. Bertozzi
  • P. Constantin


We present a proof of Chemin's [4] result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth.


Vortex Neural Network Statistical Physic Complex System Nonlinear Dynamics 
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  1. 1.
    Alinhac, S.: Remarques sur l'instabilité du problème des poches de tourbillon. Prépublication de l'Université d'Orsay, à paraitre dans J. Funct. Anal. 1989.Google Scholar
  2. 2.
    Bertozzi, A.: Existence, Uniqueness, and a Characterization of Solutions to the Contour Dynamics Equation. PhD thesis, Princeton University 1991Google Scholar
  3. 3.
    Buttke, T.F.: The observation of singularities in the boundary of patches of constant vorticity. Phys. Fluids A1, 1283–1285 (1989)Google Scholar
  4. 4.
    Chemin, J.-Y.: Persistance de structures geometriques dans les fluides incompressibles bidimensionnels. Preprint 1991Google Scholar
  5. 5.
    Constantin, P., Lax, P.D., Majda, A.: A simple one dimensional model for the three dimensional vorticity equation. Commun. Pure Applied Math.38, 715–724 (1985)Google Scholar
  6. 6.
    Constantin, P. and Titi, E.S.: On the evolution of nearly circular vortex patches. Commun. Math. Phys.119, 177–198 (1988)Google Scholar
  7. 7.
    Dritschel, D.G., McIntyre, M.E.: Does contour dynamics go singular? Phys. Fluids A,2(5) 748–753 (1990)Google Scholar
  8. 8.
    Majda, A.: Vorticity and the mathematical theory of incompressible fluid flow. Commun. Pure Appl. Math.39, 5187–5220 (1986)Google Scholar
  9. 9.
    Torchinsky, A.: Real Variable Methods in Harmonic Analysis. New York: Academic Press 1986Google Scholar
  10. 10.
    Yudovich, V.I.: Non-stationary flow of an ideal incompressible liquid. Zh. Vych. Mat.3, 1032–1066 (1963) (in Russian)Google Scholar
  11. 11.
    Zabusky, N., Hughes, M.H., Roberts, K.V.: Contour dynamics for the Euler equations in two dimensions. J. Comp. Phys. 96–106 (1979)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. L. Bertozzi
    • 1
  • P. Constantin
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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