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

doi:10.1016/S0252-9602(14)60101-6

Abstract

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

LEI Yuan-Jie. THE NON-CUTOFF BOLTZMANN EQUATION WITH POTENTIAL FORCE IN THE WHOLE SPACE[J].Acta mathematica scientia,Series B, 2014, 34(5): 1519-1539.

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