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Representation of the Vortex Sheets in the Perfect Fluid

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Abstract

We discuss representation of the vortex sheets in the perfect fluid. In the preface of his book, I. Imai claimed “hyperfunction = vortex layer”, the proof of which had not been given. In 2009, K. Uchikoshi-Y. Noro gave a hyperfunctional representation of the vortex layers in the 2-dimensional fluid. Their idea being highly dependent on identifying the two dimensional Euclidean plane with the complex plane, it is difficult to interpret their representation in the real fluid phenomena. Its 3-dimensional extension was also difficult. To solve these problems, we give a new representation of the vortex sheets (or layers) by the real flow velocity vectors, whose other merits are also discussed.

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References

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Authors and Affiliations

  1. Department of Mathematics, National Defense Academy of Japan, 1-10-20, Hashirimizu, Yokosuka, Kanagawa,  239-8686, Japan

    Takashi Takiguchi

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  1. Takashi Takiguchi
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Correspondence to Takashi Takiguchi.

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The author declares that he has no conflict of interest.

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Communicated by Y. Giga

Supported in part by JSPS Grant-in-Aid for Scientific Research (C) 26400184.

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Takiguchi, T. Representation of the Vortex Sheets in the Perfect Fluid. J. Math. Fluid Mech. 20, 2161–2175 (2018). https://doi.org/10.1007/s00021-018-0403-4

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  • DOI: https://doi.org/10.1007/s00021-018-0403-4

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