2017/07/19 by Hans Lindblad, Lindblad, Hans, Martin Taylor +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.1707.06079
openalex publication_date 2017/07/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Minkowski space is shown to be globally stable as a solution to the massive\nEinstein--Vlasov system. The proof is based on a harmonic gauge in which the\nequations reduce to a system of quasilinear wave equations for the metric,\nsatisfying the weak null condition, coupled to a transport equation for the\nVlasov particle distribution function. Central to the proof is a collection of\nvector fields used to control the particle distribution function, a function of\nboth spacetime and momentum variables. The vector fields are derived using a\ngeneral procedure, are adapted to the geometry of the solution and reduce to\nthe generators of the symmetries of Minkowski space when restricted to acting\non spacetime functions. Moreover, when specialising to the case of vacuum, the\nproof provides a simplification of previous stability works.\n