Global existence of bounded solutions to the relativistic BGK model

The relativistic BGK model is a representative relaxation-time approximation of the relativistic Boltzmann equation. In this paper, we prove the global existence of bounded solutions to the relativistic BGK model proposed by Anderson and Witting when the initial data satisfies the excess conservatio...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2022-02, Vol.63, p.103409, Article 103409
Main Author: Hwang, Byung-Hoon
Format: Article
Language:English
Subjects:
Anderson–Witting model
Bounded solution
Global existence
Relativistic BGK model
Relativistic Boltzmann equation
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Summary:The relativistic BGK model is a representative relaxation-time approximation of the relativistic Boltzmann equation. In this paper, we prove the global existence of bounded solutions to the relativistic BGK model proposed by Anderson and Witting when the initial data satisfies the excess conservations of mass and energy, and the excess entropy inequality from global equilibrium. The L∞ estimate established in Guo (2010) is the main ingredient of the proof.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2021.103409