Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics called the Motsch-Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solutions towards the equilibrium under suitable assumptions on the initial data. We also remark that the rate of convergence is exponential when the spatial domain is periodic. The main methods used in this paper are the classical energy estimates combined with hyperbolic-parabolic dissipation arguments.

Original languageEnglish
Pages (from-to)1887-1916
Number of pages30
JournalNonlinearity
Volume29
Issue number7
DOIs
Publication statusPublished - 2016 May 25

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces'. Together they form a unique fingerprint.

  • Cite this