• Medientyp: E-Artikel
  • Titel: Asymptotic analysis of Vlasov-type equations under strong local alignment regime
  • Beteiligte: Kang, Moon-Jin; Vasseur, Alexis F.
  • Erschienen: World Scientific Pub Co Pte Ltd, 2015
  • Erschienen in: Mathematical Models and Methods in Applied Sciences, 25 (2015) 11, Seite 2153-2173
  • Sprache: Englisch
  • DOI: 10.1142/s0218202515500542
  • ISSN: 0218-2025; 1793-6314
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  • Beschreibung: 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.