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On the Dynamics of Navier-Stokes and Euler Equations

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Abstract

This is a detailed study on certain dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a) zero viscosity limit of the spectra of linear Navier-Stokes operator, (b) heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Due to the difficulty of the problem for the full Navier-Stokes and Euler equations, we also propose and study two simpler models of them.

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Author notes

  1. Yueheng Lan

    Present address: Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA, 93106-5070, USA

Authors and Affiliations

  1. Department of Chemistry, University of North Carolina, Chapel Hill, NC, 27599-3290, USA

    Yueheng Lan

  2. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    Y. Charles Li

Authors
  1. Yueheng Lan
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  2. Y. Charles Li
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Correspondence to Y. Charles Li.

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Lan, Y., Li, Y.C. On the Dynamics of Navier-Stokes and Euler Equations. J Stat Phys 132, 35–76 (2008). https://doi.org/10.1007/s10955-008-9555-6

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  • DOI: https://doi.org/10.1007/s10955-008-9555-6

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