Dynamics of a spatially homogeneous Vicsek model for oriented particles on the plane
Analysis of PDEs
2016-08-02 v1
Abstract
We consider a spatially homogeneous Kolmogorov-Vicsek model in two dimensions, which describes the alignment dynamics of self-driven stochastic particles that move on the plane at a constant speed, under space-homogeneity. In \cite{F-K-M}, Alessio Figalli and the authors have shown the existence of global weak solutions for this two-dimensional model. However, no time-asymptotic behavior has been obtained for the two-dimensional case, due to the failure of the celebrated Bakery and Emery condition for the logarithmic Sobolev inequality. We prove exponential convergence (with quantitative rate) of the weak solutions towards a Fisher-von Mises distribution, using a new condition for the logarithmic Sobolev inequality.
Keywords
Cite
@article{arxiv.1608.00185,
title = {Dynamics of a spatially homogeneous Vicsek model for oriented particles on the plane},
author = {Moon-Jin Kang and Javier Morales},
journal= {arXiv preprint arXiv:1608.00185},
year = {2016}
}