Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry

DOI10.1016/j.jde.2017.02.004zbMath1365.35182arXiv1506.02440OpenAlexW643645065MaRDI QIDQ515506

Ho Lee, Ernesto Nungesser

Publication date: 16 March 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.02440

zbMATH Keywords

classical solutionglobal in time solutioncollision operatorexistence and uniqueness resulttheoretical cosmologyEinstein-Vlasov systemBianchi I symmetryEinstein-Bolzmann system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Relativistic cosmology (83F05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Einstein equations (35Q76) Vlasov equations (35Q83) Boltzmann equations (35Q20) PDEs in connection with astronomy and astrophysics (35Q85)

Related Items (11)

Small solutions of the Einstein–Boltzmann-scalar field system with Bianchi symmetry ⋮ On almost Ehlers–Geren–Sachs theorems ⋮ Bianchi I solutions of the Einstein-Boltzmann system with a positive cosmological constant ⋮ The coupled Yang-Mills-Boltzmann system in Bianchi type I space-time ⋮ Kantowski–Sachs cosmology with Vlasov matter ⋮ The massless Einstein–Boltzmann system with a conformal gauge singularity in an FLRW background ⋮ Late-time behaviour of Israel particles in a FLRW spacetime with \(\Lambda>0\) ⋮ Self-similarity breaking of cosmological solutions with collisionless matter ⋮ Asymptotic behaviour of the Boltzmann equation as a cosmological model ⋮ On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology ⋮ The spatially homogeneous Boltzmann equation for massless particles in an FLRW background

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coordinates in the relativistic Boltzmann theory
• Bianchi cosmologies with anisotropic matter: locally rotationally symmetric models
• Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data
• Global existence of solutions for the Einstein-Boltzmann system with cosmological constant in the Robertson-Walker space-time
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• Cosmic censorship for some spatially homogeneous cosmological models
• Existence, uniqueness, and local stability for the Einstein-Maxwell- Boltzmann system
• Instability of spatially homogeneous solutions in the class of \(\mathbb T^2\)-symmetric solutions to Einstein's vacuum equations
• Asymptotic stability of the relativistic Maxwellian
• Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi type I space-time
• Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson-Walker spacetime
• THE EINSTEIN–BOLTZMANN SYSTEM AND POSITIVITY
• Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI
• Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Global solutions of the Vlasov-Poisson-Boltzmann system in a cosmological setting
• Global existence of solutions for the Einstein–Boltzmann system in a Bianchi type I spacetime for arbitrarily large initial data
• Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant
• The Spatially Homogeneous Relativistic Boltzmann Equation with a Hard Potential
• The Vlasov-Poisson-Boltzmann system near vacuum

This page was built for publication: Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry