Coordinates in the relativistic Boltzmann theory

Abstract

It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illustrate how to derive an assortment coordinates in which to represent the relativistic Boltzmann collision operator. We show the equivalence between some known representations, and others which seem to be new. One of these representations has been used recently to solve several open problems.

16 pages, to appear in the issue of K.R.M. dedicated to the memory of Carlo Cercignani

References in corpus (3)

• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum
• The Newtonian limit of the relativistic Boltzmann equation

Cited by in corpus (8)

• The Einstein-Vlasov System/Kinetic Theory
• Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System
• Hilbert Expansion from the Boltzmann equation to relativistic Fluids
• An introduction to the relativistic kinetic theory on curved spacetimes
• 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
• The relativistic quantum Boltzmann equation near equilibrium
• On the Determinant Problem for the Relativistic Boltzmann Equation