Application of relativistic thermodynamics shows global existence of classical solutions in polyatomic gases, indicating behavior near equilibrium.
In this paper, we consider the direct application of the relativistic extended thermodynamics theory of polyatomic gases developed in [Ann. Phys. 377 (2017) 414--445] to the relativistic BGK model proposed by Marle. We present the perturbed Marle model around the generalized J\"{u}ttner distribution and investigate the properties of the linear operator. Then we prove the global existence and large-time behavior of classical solutions when the initial data is sufficiently close to a global equilibrium.
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Byung-Hoon Hwang (2025) studied this question.
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