Calculus of Variations and Geometric Measure Theory

A. Figalli - M. J. Kang - J. Morales

Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow

created by figalli on 15 Aug 2017


Accepted Paper

Inserted: 15 aug 2017
Last Updated: 15 aug 2017

Journal: Arch. Ration. Mech. Anal.
Year: 2017


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.