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

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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.
Publisher
SPRINGER
Issue Date
2018-03
Language
English
Article Type
Article
Citation

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.227, no.3, pp.869 - 896

ISSN
0003-9527
DOI
10.1007/s00205-017-1176-2
URI
http://hdl.handle.net/10203/278718
Appears in Collection
MA-Journal Papers(저널논문)
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