Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

Abstract

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L_{\ell }^{\infty }$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{ń}ski and Ekiel-Je{ż}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.

arXiv comment64 pages

References in corpus (4)

• Decay and Continuity of Boltzmann Equation in Bounded Domains
• Global Classical Solutions of the Boltzmann Equation with Long-Range Interactions and Soft Potentials
• Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum
• The Newtonian limit of the relativistic Boltzmann equation

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