Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (5): 1519-1539.doi: 10.1016/S0252-9602(14)60101-6

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THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE

 LEI Yuan-Jie   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2013-03-13 Revised:2013-05-20 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    This work was supported by the Fundamental Research Funds for the Central Universities.

Abstract:

This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1–3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].

Key words: non-cutoff Boltzmann, potential force,  global existence, convergence rates

CLC Number: 

  • 35A05
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