Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

Details Cauchy problem for the Boltzmann-BGK model near a global Maxwellian Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

2010-09-28

arxiv.org/abs/1009.5570v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.

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