A Collision-Avoiding flocking particle system proposed in [8] is studied inthis paper. The global wellposedness of its corresponding Vlasov-type kineticequation is proved. As a corollary of the global stability result, the meanfield limit of the particle system is obtained. Furthermore, thetime-asymptotic flocking behavior of the solution to the kinetic equation isalso derived. The technics used for local wellposedness and stability followfrom similar ideas to those have been used in [3,22,14]. While in order toextend the local result globally, the main contribution here is to generate aseries of new estimates for this Vlasov type equation, which imply that thegrowing of the characteristics can be controlled globally. Further estimatesalso show the long time flocking phenomena.
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