On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
Artikel i vetenskaplig tidskrift, 2018

The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global-in-time solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in finite time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.

Cosmological expansion

Blow-up

Global existence

Asymptotic behavior

Einstein-Vlasov-Fokker-Planck

Författare

Simone Calogero

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

S. Pankavich

Colorado School of Mines

Kinetic and Related Models

1937-5093 (ISSN) 1937-5077 (eISSN)

Vol. 11 5 1063-1083

Ämneskategorier

Beräkningsmatematik

Annan fysik

Matematisk analys

DOI

10.3934/krm.2018041