Asymptotic analysis of Vlasov-type equations under strong local alignment regime

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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 [On strong local alignment in the kinetic Cucker-Smale model, in Hyperbolic Conservation Laws and Related Analysis with Applications, Springer Proceedings in Mathematics & Statistics, Vol. 49 (Springer, 2014), pp. 227-242], as a singular limit of an alignment force proposed by Motsch and Tadmor in [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 141 (2011) 923-947]. As the local alignment strongly dominates, 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.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2015-10
Language
English
Article Type
Article
Citation

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, v.25, no.11

ISSN
0218-2025
DOI
10.1142/S0218202515500542
URI
http://hdl.handle.net/10203/278723
Appears in Collection
MA-Journal Papers(저널논문)
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