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.

64 pages

Cited by in corpus (11)

• Coordinates in the relativistic Boltzmann theory
• Hilbert Expansion from the Boltzmann equation to relativistic Fluids
• Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• The relativistic quantum Boltzmann equation near equilibrium
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• Relaxation time approximation revisited and non-analytical structure in retarded correlators
• The spatially homogeneous Boltzmann equation for massless particles in an FLRW background
• Normal mode analysis within a mutilated relaxation time approximation
• On the Determinant Problem for the Relativistic Boltzmann Equation
• Normal mode analysis within relativistic massive transport