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Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow

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Abstract

We consider the so-called spatially homogenous Kolmogorov–Vicsek model, a non-linear Fokker–Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

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Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, Rämistrasse 101, Zurich, 8092, Switzerland

    Alessio Figalli

  2. Department of Mathematics, Sookmyung Women’s University, Seoul, 04310, Korea

    Moon-Jin Kang

  3. Department of Mathematics, The University of Texas at Austin, Speedway 2515 Stop C1200, Austin, TX, 78712, USA

    Javier Morales

Authors
  1. Alessio Figalli
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  2. Moon-Jin Kang
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  3. Javier Morales
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Corresponding author

Correspondence to Moon-Jin Kang.

Additional information

Communicated by F. Otto

Corresponding author: Moon-Jin Kang.

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Figalli, A., Kang, MJ. & Morales, J. Global Well-posedness of the Spatially Homogeneous Kolmogorov–Vicsek Model as a Gradient Flow. Arch Rational Mech Anal 227, 869–896 (2018). https://doi.org/10.1007/s00205-017-1176-2

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  • DOI: https://doi.org/10.1007/s00205-017-1176-2

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