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Microscopic Expression of Anomalous Dissipation in Passive Scalar Transport

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Abstract

We study anomalous dissipation from a microscopic viewpoint. In the work by Drivas et al. (Arch Ration Mech Anal 243(3):1151–1180, 2022), the property of anomalous dissipation provides the existence of non-unique weak solutions for a transport equation with a singular velocity field. In this paper, we reconsider this solution in terms of kinetic theory and clarify its microscopic property. Consequently, energy loss can be expressed by non-vanishing microscopic obstruction.

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Funding

We would like to thank Professor Yoshikazu Giga for valuable comments on this work. Research of TT was partly supported by the JSPS Grant-in-Aid for JSPS Research Fellows 22J10745. Research of TY was partly supported by the JSPS Grants-in-Aid for Scientific Research 20H01819.

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Authors and Affiliations

  1. Tokyo, Japan

    Tomonori Tsuruhashi

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

    Tsuyoshi Yoneda

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  1. Tomonori Tsuruhashi
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  2. Tsuyoshi Yoneda
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Correspondence to Tsuyoshi Yoneda.

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Communicated by Y. Giga.

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Tsuruhashi, T., Yoneda, T. Microscopic Expression of Anomalous Dissipation in Passive Scalar Transport. J. Math. Fluid Mech. 26, 5 (2024). https://doi.org/10.1007/s00021-023-00834-3

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  • DOI: https://doi.org/10.1007/s00021-023-00834-3

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