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2006, Volume 16, Issue 1: 253-277. Doi: 10.3934/dcds.2006.16.253
This issue Previous Article Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction Next Article Preface

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

  • 1.

    Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

  • 2.

    Liu Bie Ju Centre of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

  • 3.

    Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079

Received:  May 2005
Revised:  February 2006
Published:  March 2006
Abstract / Introduction Related Papers Cited by
    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.
    Mathematics Subject Classification: 76P05, 82C40, 74G25.

    Citation:
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