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 $L^{\infty }$ estimate established in Guo (2010) is the main ingredient of the proof.

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相对论BGK模型的有界解的全局存在性

相对论 BGK 模型是相对论玻尔兹曼方程的典型弛豫时间近似。在本文中，我们证明了当初始数据满足质量和能量的过剩守恒以及全局平衡的过剩熵不等式时，Anderson 和 Witting 提出的相对论 BGK 模型的有界解的全局存在性。这${升}^{\infty }$ 郭（2010）建立的估计是证明的主要成分。