Existence of weak solutions to kinetic flocking models

TL;DR

This paper proves the global existence of weak solutions for various kinetic flocking models, including Cucker-Smale and Motsch-Tadmor, using advanced mathematical tools like the velocity averaging lemma.

Contribution

It establishes the existence of weak solutions for a broad class of kinetic flocking equations, including new models with non-symmetric potentials.

Findings

Proved global existence of weak solutions for kinetic flocking models.

Extended results to models with non-symmetric potentials and local alignment.

Applied mathematical tools such as the velocity averaging lemma and Schauder fixed point theorem.

Abstract

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.