Global existence and uniqueness of measure valued solutions to a Vlasov‐type equation with local alignment

摘要

> We use a particle method to study a Vlasov‐type equation with local alignment, which was proposed by Sebastien Motsch and Eitan Tadmor [ J. Statist. Phys. , 141(2011), pp. 923‐947]. For N ‐particle system, we study the unconditional flocking behavior for a weighted Motsch‐Tadmor model and a model with a “tail”. When N goes to infinity, global existence and stability (hence uniqueness) of measure valued solutions to the kinetic equation of this model are obtained. We also prove that measure valued solutions converge to a flock. The main tool we use in this paper is Monge‐Kantorovich‐Rubinstein distance.