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Asymptotic Expansions for the Lagrangian Trajectories from Solutions of the Navier–Stokes Equations

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Abstract

Consider any Leray–Hopf weak solution of the three-dimensional Navier–Stokes equations for incompressible, viscous fluid flows. We prove that any Lagrangian trajectory associated with such a velocity field has an asymptotic expansion, as time tends to infinity, which describes its long-time behavior very precisely.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX, 79409-1042, USA

    Luan Hoang

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  1. Luan Hoang
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Correspondence to Luan Hoang.

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Communicated by A. Ionescu

Dedicated to the memory of Ciprian Foias (1933–2020)

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Hoang, L. Asymptotic Expansions for the Lagrangian Trajectories from Solutions of the Navier–Stokes Equations. Commun. Math. Phys. 383, 981–995 (2021). https://doi.org/10.1007/s00220-020-03863-5

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  • DOI: https://doi.org/10.1007/s00220-020-03863-5

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