Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

Abstract

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c\ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to \infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon }$ for any $\epsilon \in (0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.

35 pages

References in corpus (1)

• Global Existence Proof for Relativistic Boltzmann Equation with Hard Interactions

Cited by in corpus (13)

• The Einstein-Vlasov System/Kinetic Theory
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Coordinates in the relativistic Boltzmann theory
• Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System
• Hilbert Expansion from the Boltzmann equation to relativistic Fluids
• Large-Time Decay of the Soft Potential relativistic Boltzmann equation in ${\mathbb{R}}_x^3$
• Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry
• On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics
• Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system
• Anderson-Witting model of the relativistic Boltzmann equation near equilibrium
• The relativistic quantum Boltzmann equation near equilibrium
• On the Determinant Problem for the Relativistic Boltzmann Equation
• Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials