The stability of the Minkowski space for the Einstein-Vlasov system

DOI10.2140/apde.2021.14.425zbMath1476.83007arXiv1707.06141OpenAlexW2983020253MaRDI QIDQ5919100

Jacques Smulevici, David Fajman, Jérémie Joudioux

Publication date: 29 September 2021

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.06141

zbMATH Keywords

Einstein equationsgeneral relativityrelativistic kinetic theory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Equations of motion in general relativity and gravitational theory (83C10) Minkowski geometries in nonlinear incidence geometry (51B20) Vlasov equations (35Q83)

Related Items (26)

Sharp decay estimates for the Vlasov-Poisson and Vlasov-Yukawa systems with small data ⋮ An introduction to the relativistic kinetic theory on curved spacetimes ⋮ Global nonlinear stability of large dispersive solutions to the Einstein equations ⋮ The Einstein-Vlasov system in maximal areal coordinates-local existence and continuation ⋮ Static Solutions to the Spherically Symmetric Einstein–Vlasov System: A Particle Number–Casimir Approach ⋮ Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes ⋮ Exterior stability of Minkowski space in generalized harmonic gauge ⋮ The constraint equations of the Einstein-Vlasov-Maxwell system in the maximal-isotropic coordinates ⋮ Stable cosmologies with collisionless charged matter ⋮ Nonlinear stability of self-gravitating massive fields. A wave-Klein–Gordon model ⋮ Global existence of a nonlinear wave equation arising from Nordström's theory of gravitation ⋮ Small data solutions for the Vlasov-Poisson system with a repulsive potential ⋮ Future stability of expanding spatially homogeneous FLRW solutions of the spherically symmetric Einstein–massless Vlasov system with spatial topology R3 ⋮ Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model ⋮ Optimal decay estimates for the Vlasov-Poisson system with radiation damping ⋮ The Vlasov–Poisson–Landau system in the weakly collisional regime ⋮ Existence globale de solutions au système sphériquement symétrique de Einstein-Vlasov-Maxwell ⋮ Stability of vacuum for the Landau equation with hard potentials ⋮ Global existence of solutions to the spherically symmetric Einstein-Vlasov-Maxwell system ⋮ Einstein-Klein-Gordon spacetimes in the harmonic near-Minkowski regime ⋮ Global Classical Solutions for the Vlasov--Nordström--Fokker--Planck System ⋮ Characteristic Cauchy problem on the light cone for the Einstein–Vlasov system in temporal gauge ⋮ Asymptotic stability of Minkowski space-time with non-compactly supported massless Vlasov matter ⋮ Sharp decay estimates for the Vlasov-Poisson system with an external magnetic field ⋮ Propagation of regularity and long time behavior of the \(3D\) Massive relativistic transport equation. II: Vlasov-Maxwell system ⋮ Phase mixing for solutions to 1D transport equation in a confining potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global solutions of the Euler-Maxwell two-fluid system in 3D
• Global existence for coupled Klein-Gordon equations with different speeds
• Global solutions of quasilinear systems of Klein-Gordon equations in 3D
• Models for self-gravitating photon shells and geons
• On the asymptotic behavior of solutions to the Einstein vacuum equations in wave coordinates
• Dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data
• Existence of axially symmetric static solutions of the Einstein-Vlasov system
• Orbital stability of spherical galactic models
• Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data
• Cauchy problems for the conformal vacuum field equations in general relativity
• Nonlinear stability of the Milne model with matter
• The global stability of Minkowski space-time in harmonic gauge
• Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data
• Absence of shocks in an initially dilute collisionless plasma
• Global existence of solutions of the spherically symmetric Vlasov- Einstein system with small initial data
• On the proof of the positive mass conjecture in general relativity
• Lectures on nonlinear hyperbolic differential equations
• A new proof of the positive energy theorem.
• Small data solutions of the Vlasov-Poisson system and the vector field method
• The global nonlinear stability of Minkowski space for the massless Einstein-Vlasov system
• A commuting-vector-field approach to some dispersive estimates
• Global existence for the Einstein vacuum equations in wave coordinates
• An intrinsic hyperboloid approach for Einstein Klein-Gordon equations
• Sharp asymptotics for the solutions of the three-dimensional massless Vlasov-Maxwell system with small data
• Rotating, stationary, axially symmetric spacetimes with collisionless matter
• Global solutions of the Einstein-Maxwell equations
• Global stability of Minkowski space for the Einstein-Vlasov system in the harmonic gauge
• The nonvacuum Einstein flow on surfaces of negative curvature and nonlinear stability
• A vector field method for relativistic transport equations with applications
• A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
• On the asymptotics for the vacuum Einstein constraint equations
• Problème de Cauchy pour le système intégro-différentiel d'Einstein-Liouville. (Cauchy problem for the Einstein-Liouville integro-differential system)
• The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system
• A NOTE ON THE COLLAPSE OF SMALL DATA SELF-GRAVITATING MASSLESS COLLISIONLESS MATTER
• Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Blow-up for quasi-linear wave equations in three space dimensions
• Remark on the asymptotic behavior of the klein gordon equation in ℝⁿ⁺¹
• Static solutions of the spherically symmetric Vlasov–Einstein system
• Existence of non-trivial, vacuum, asymptotically simple spacetimes
• Global Solution for Massive Maxwell‐Klein‐Gordon Equations
• Static Solutions to the Einstein--Vlasov System with a Nonvanishing Cosmological Constant
• The Global Nonlinear Stability of Minkowski Space for Self-Gravitating Massive Fields
• Static solutions of the Vlasov-Einstein system
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

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