Relativistic BGK model for massless particles in the FLRW spacetime

Byung-Hoon Hwang; Ho Lee; Seok-Bae Yun

doi:10.3934/krm.2021031

Article Contents

2021, Volume 14, Issue 6: 949-959. Doi: 10.3934/krm.2021031

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Relativistic BGK model for massless particles in the FLRW spacetime

1.
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
2.
Department of Mathematics and Research Institute for Basic Science, Kyung Hee University, Seoul, 02447, Republic of Korea

Received: March 31, 2021

Revised: July 31, 2021

Early access: September 2021

Published: December 2021

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In this paper, we address the Cauchy problem for the relativistic BGK model proposed by Anderson and Witting for massless particles in the Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime. We first derive the explicit form of the Jüttner distribution in the FLRW spacetime, together with a set of nonlinear relations that leads to the conservation laws of particle number, momentum, and energy for both Maxwell-Boltzmann particles and Bose-Einstein particles. Then, we find sufficient conditions that guarantee the existence of equilibrium coefficients satisfying the nonlinear relations and we show that the condition is satisfied through all the induction steps once it is verified for the initial step. Using this observation, we construct explicit solutions of the relativistic BGK model of Anderson-Witting type for massless particles in the FLRW spacetime.

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Mathematics Subject Classification: 76P05, 83C10, 82C40, 35A01.

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