Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale Model
Analysis of PDEs
2017-04-25 v1
Abstract
We first prove the well-posedness of weak and strong solutions to the kinetic Cucker-Smale model in the Sobolev space with the initial data having compact velocity support. Then we study the kinetic Cucker-Smale model with noise. By introducing two weighted Hilbert spaces, we successfully establish the well-posedness of weak and strong solutions, respectively. Our proof is based on weighted energy estimates. Finally, we rigorously justify the vanishing noise limit.
Keywords
Cite
@article{arxiv.1704.07027,
title = {Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale Model},
author = {Chunyin Jin},
journal= {arXiv preprint arXiv:1704.07027},
year = {2017}
}