Global well-posedness for the Fokker-Planck-Boltzmann equation in Besov-Chemin-Lerner type spaces

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)8638-8674
Journal / PublicationJournal of Differential Equations
Volume260
Issue number12
Publication statusPublished - 15 Jun 2016

Abstract

In this paper, motivated by [16], we use the Littlewood-Paley theory to establish some estimates on the nonlinear collision term, which enable us to investigate the Cauchy problem of the Fokker-Planck-Boltzmann equation. When the initial data is a small perturbation of the Maxwellian equilibrium state, under the Grad's angular cutoff assumption, the unique global solution for the hard potential case is obtained in the Besov-Chemin-Lerner type spaces C([0, ∞); L~ξ 2(B2,r s)) with 1 ≤ r ≤ 2 and s > 3/2 or s = 3/2 and r = 1. Besides, we also obtain the uniform stability of the dependence on the initial data.

Research Area(s)

  • Cauchy problem, Cutoff assumption, Fokker-Planck-Boltzmann equation, Hard potential, Littlewood-Paley theory