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Global regularity for vortex patches

Abstract

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.

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References

  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.

  2. Bertozzi, A.: Existence, Uniqueness, and a Characterization of Solutions to the Contour Dynamics Equation. PhD thesis, Princeton University 1991

  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. Chemin, J.-Y.: Persistance de structures geometriques dans les fluides incompressibles bidimensionnels. Preprint 1991

  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. Constantin, P. and Titi, E.S.: On the evolution of nearly circular vortex patches. Commun. Math. Phys.119, 177–198 (1988)

    Google Scholar 

  7. Dritschel, D.G., McIntyre, M.E.: Does contour dynamics go singular? Phys. Fluids A,2(5) 748–753 (1990)

    Google Scholar 

  8. Majda, A.: Vorticity and the mathematical theory of incompressible fluid flow. Commun. Pure Appl. Math.39, 5187–5220 (1986)

    Google Scholar 

  9. Torchinsky, A.: Real Variable Methods in Harmonic Analysis. New York: Academic Press 1986

    Google Scholar 

  10. Yudovich, V.I.: Non-stationary flow of an ideal incompressible liquid. Zh. Vych. Mat.3, 1032–1066 (1963) (in Russian)

    Google Scholar 

  11. Zabusky, N., Hughes, M.H., Roberts, K.V.: Contour dynamics for the Euler equations in two dimensions. J. Comp. Phys. 96–106 (1979)

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Partially supported by a National Science Foundation Postdoctoral Fellowship

Partially supported by the National Science Foundation

Communicated by A. Jaffe

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Bertozzi, A.L., Constantin, P. Global regularity for vortex patches. Commun.Math. Phys. 152, 19–28 (1993). https://doi.org/10.1007/BF02097055

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  • DOI: https://doi.org/10.1007/BF02097055

Keywords

  • Vortex
  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics