The flocking behavior of the infinite-particle Cucker-Smale model

In this article, we study the flocking behavior of the solutions to the infinite-particle Cucker-Smale model. We first establish the existence and uniqueness of the solutions to the infinite-particle Cucker-Smale model. And then build the boundedness of velocity by showing the non-increase of the l_\infty-norm of v(t) through classifying the particles according to the norm of velocity. Finally, we obtain the flocking behavior of the infinite-particle Cucker-Smale model. More precisely, the solutions to the infinite-particle Cucker-Smale model will concentrate exponentially fast in velocity to the average of the initial velocity, while in space the position differences between particles will be uniformly bounded.