Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum

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

28 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)253-277
Journal / PublicationDiscrete and Continuous Dynamical Systems
Volume16
Issue number1
Publication statusPublished - Sep 2006

Abstract

In this paper, we study the Cauchy problem for the Boltzmann equation with an external force and the Vlasov-Poisson-Boltzmann system in infinite vacuum. The global existence of solutions is first proved for the Boltzmann equation with an external force which is integrable with respect to time in some sense under the smallness assumption on initial data in weighted norms. For the Vlasov-Poisson-Boltzmann system, the smallness assumption on initial data leads to the decay of the potential field which in turn gives the global existence of solutions by the result on the case with external forces and an iteration argument. The results obtained here generalize those previous works on these topics and they hold for a class of general cross sections including the hard-sphere model.

Research Area(s)

  • Boltzmann equation, Classical solutions, Global existence, Vlasov-Poisson-Boltzmann system