Existence of weak solutions to kinetic flocking models

We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under consideration include the kinetic Cucker-Smale equation with possibly non-symmetric flocking potential, the Cucker-Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor. The main tools employed in the analysis are the velocity averaging lemma and the Schauder fixed point theorem along with various integral bounds.