Asymptotic-stability of the inhomogeneous Boltzmann equation in the Robertson–Walker space–time with Israel particles

ABSTRACT

In this paper, we consider the Cauchy problem for the spatially inhomogeneous relativistic Boltzmann equation where the collision kernel is generated by Israel particle. Unique global (in time) classical solution is obtained in a suitable weighted space by considering small initial data and the Robertson–Walker space–time as background. We also studied the asymptotic behaviour of the solutions as well as the $L^{\mathrm{\infty }}$-stability.

KEYWORDS:

• Inhomogeneous relativistic Boltzmann equation
• Israel particles
• classical solution
• asymptotic behaviour
• $L^{\mathrm{\infty }}$-stability

AMS SUBJECT CLASSIFICATIONS:

• 76P05
• 35Q20

Disclosure statement

No potential conflict of interest was reported by the authors.