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Locality of Vortex Stretching for the 3D Euler Equations

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Abstract

We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.

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Acknowledgements

Research of YS was partially supported by Grant-in-Aid for JSPS Fellows 21J00025, Japan Society for the Promotion of Science (JSPS). Research of TY was partly supported by the JSPS Grants-in-Aid for Scientific Research 20H01819.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1 Meguro, Tokyo, 153-8914, Japan

    Yuuki Shimizu

  2. Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8601, Japan

    Tsuyoshi Yoneda

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  1. Yuuki Shimizu
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  2. Tsuyoshi Yoneda
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Correspondence to Tsuyoshi Yoneda.

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Communicated by S. Shkoller.

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Shimizu, Y., Yoneda, T. Locality of Vortex Stretching for the 3D Euler Equations. J. Math. Fluid Mech. 25, 18 (2023). https://doi.org/10.1007/s00021-023-00763-1

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  • DOI: https://doi.org/10.1007/s00021-023-00763-1

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