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We study the global existence and uniqueness of weak solutions to kineticKolmogorov-Vicsek models that can be considered a non-local non-linearFokker-Planck type equation describing the dynamics of individuals withorientational interactions. This model is derived from the discreteCouzin-Vicsek algorithm as mean-field limit \cite{B-C-C,D-M}, which governs theinteractions of stochastic agents moving with a velocity of constant magnitude,i.e. the the corresponding velocity space for these type of Kolmogorov-Vicsekmodels are the unit sphere. Our analysis for $L^p$ estimates and compactnessproperties take advantage of the orientational interaction property meaningthat the velocity space is a compact manifold.

Global weak solutions for Kolmogorov-Vicsek type equations with orientational interactions