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

2015/09/08 by Alessio Figalli, Moon-Jin Kang, Figalli, Alessio +3
Environmental Science · Mathematics · Economics, Econometrics and Finance · #Ecosystem dynamics and resilience #Mathematical Biology Tumor Growth #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1509.02599

Abstract

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

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