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Global existence and uniqueness to the Cauchy problem of the BGK equation with infinite energy
Author(s) -
Chen Zili,
Zhang Xianwen
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3757
Subject(s) - uniqueness , mathematics , boltzmann equation , lemma (botany) , mathematical analysis , uniqueness theorem for poisson's equation , initial value problem , cauchy problem , picard–lindelöf theorem , energy (signal processing) , fixed point theorem , physics , quantum mechanics , ecology , statistics , poaceae , biology
The Bhatnagar–Gross–Krook model of the Boltzmann equation is of great importance in the kinetic theory of rarefied gases. Various existence and uniqueness results have been built under the boundedness of energy. In this paper, we will establish several global existence results to the Bhatnagar–Gross–Krook equation with infinite energy. It heavily relies on a new moments lemma and a new existence and uniqueness theorem of weighted velocity‐spatial L ∞ solutions. Copyright © 2015 John Wiley & Sons, Ltd.