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Late-time behaviour of Israel particles in a FLRW spacetime with \(\Lambda>0\). (English) Zbl 1366.35111

Summary: In this paper we study the space-homogeneous Boltzmann equation in a spatially flat FLRW spacetime. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the asymptotic behaviour of solutions. The main argument of the paper is to use the energy method of Guo, and we observe that the method can be applied to study small solutions in a cosmological case. It is the first result of this type where a physically well-motivated scattering kernel is considered for the general relativistic Boltzmann equation.

MSC:

35Q20 Boltzmann equations
35B40 Asymptotic behavior of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
83F05 Relativistic cosmology
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