Asymptotic analysis of Vlasov-type equations under strong local alignment regime
Analysis of PDEs
2014-12-11 v1
Abstract
We consider the hydrodynamic limit of a collisionless and non-diffusive kinetic equation under strong local alignment regime. The local alignment is first considered by Karper, Mellet and Trivisa in [24], as a singular limit of an alignment force proposed by Motsch and Tadmor in [32]. As the local alignment strongly dominate, a weak solution to the kinetic equation under consideration converges to the local equilibrium, which has the form of mono-kinetic distribution. We use the relative entropy method and weak compactness to rigorously justify the weak convergence of our kinetic equation to the pressureless Euler system.
Keywords
Cite
@article{arxiv.1412.3119,
title = {Asymptotic analysis of Vlasov-type equations under strong local alignment regime},
author = {Moon-Jin Kang and Alexis F. Vasseur},
journal= {arXiv preprint arXiv:1412.3119},
year = {2014}
}