Contents Online
Communications in Mathematical Sciences
Volume 15 (2017)
Number 8
Existence of weak solutions to a kinetic flocking model with cut-off interaction function
Pages: 2177 – 2193
DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n8.a4
Author
Abstract
We prove the existence of weak solutions to a kinetic flocking model with cut-off interaction function by using the weak convergence method. Under the natural assumption that the $v$-support of the initial distribution function $f_0(x,v)$ is bounded, we show that the $v$-support of the distribution function $f(t,x,v)$ is uniformly bounded in time. Employing this property, we remove the constraint in the paper of Karper, Mellet, and Trivisa (SIAM. J. Math. Anal., 45, 215–243, 2013) that the initial distribution function should have better integrability for large $\lvert x \rvert$.
Keywords
Cucker–Smale model, kinetic flocking model, velocity averaging lemma, Schauder fixed point theorem
2010 Mathematics Subject Classification
35D30, 35Q83, 35Q92, 74H20
Received 29 April 2017
Accepted 23 July 2017
Published 20 December 2017