2016/06/16 by Simone Calogero, Calogero, Simone, Stephen Pankavich +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #General Relativity and Quantum Cosmology (gr-qc) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1606.05101
openalex publication_date 2016/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion\ndynamics of self-gravitating particles within the Einstein theory of general\nrelativity. We study the Cauchy problem for spatially homogeneous and isotropic\nsolutions and prove the existence of both global solutions and solutions that\nblow-up in finite time depending on the size of certain functions of the\ninitial data. We also derive information on the large-time behavior of global\nsolutions and toward the singularity for solutions which blow-up in fine time.\nOur results entail the existence of a phase of decelerated expansion followed\nby a phase of accelerated expansion, in accordance with the physical\nexpectations in cosmology.\n