Global existence and uniqueness to the Cauchy problem of the BGK equation with infinite energy |
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| Authors: | Zili Chen Xianwen Zhang |
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| Affiliation: | 1. Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi 330031, China;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China |
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| Abstract: | 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. |
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| Keywords: | BGK equation global existence uniqueness infinite energy subclass 35F25 35J05 35Q83 82C40 |
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