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Singularities of Euler Flow? Not Out of the Blue!

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Abstract

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.

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Authors and Affiliations

  1. Observatoire de la Côte d'Azur, CNRS UMR 6529, BP 4229, 06304, Nice Cedex 4, France

    U. Frisch, T. Matsumoto & J. Bec

  2. CNLS–Theoretical Division, LANL, Los Alamos, New Mexico, 87545

    U. Frisch, T. Matsumoto & J. Bec

  3. Department of Physics, Kyoto University, Kitashirakawa Oiwakecho Sakyo-ku, Kyoto, 606–8502, Japan

    T. Matsumoto

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  1. U. Frisch
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Frisch, U., Matsumoto, T. & Bec, J. Singularities of Euler Flow? Not Out of the Blue!. Journal of Statistical Physics 113, 761–781 (2003). https://doi.org/10.1023/A:1027308602344

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