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Vortex stretching and enhanced dissipation for the incompressible 3D Navier–Stokes equations

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Abstract

We consider the 3D incompressible Navier–Stokes equations under the following \(2+\frac{1}{2}\)-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove enhanced dissipation induced by such vortex-stretching.

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Notes

  1. This computation was suggested to us by one of the referees.

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Acknowledgements

The authors sincerely thank the anonymous referees for very helpful comments regarding the manuscript, which have been incorporated in the current paper. We especially thank one of the referees for kindly providing us the calculations 1.3.3, which clarifies the situation. We thank Professors A. Mazzucato and T. Drivas for inspiring communications and telling us about the articles [8] and [13], respectively. We are also grateful to Professors P. Constantin and T. Elgindi for valuable comments. Research of TY was partially supported by Grant-in-Aid for Young Scientists A (17H04825), Grant-in-Aid for Scientific Research B (15H03621, 17H02860, 18H01136 and 18H01135), Japan Society for the Promotion of Science (JSPS). IJ has been supported by a KIAS Individual Grant MG066202 at Korea Institute for Advanced Study, the Science Fellowship of POSCO TJ Park Foundation, and the National Research Foundation of Korea grant No. 2019R1F1A1058486.

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Authors and Affiliations

  1. School of Mathematics, Korea Institute for Advanced Study, Seoul, South Korea

    In-Jee Jeong

  2. Department of Mathematics, University of Tokyo, Tokyo, Japan

    Tsuyoshi Yoneda

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  1. In-Jee Jeong
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  2. Tsuyoshi Yoneda
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Correspondence to In-Jee Jeong.

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Communicated by Y. Giga.

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Jeong, IJ., Yoneda, T. Vortex stretching and enhanced dissipation for the incompressible 3D Navier–Stokes equations. Math. Ann. 380, 2041–2072 (2021). https://doi.org/10.1007/s00208-020-02019-z

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  • DOI: https://doi.org/10.1007/s00208-020-02019-z

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