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- Title
ON THE SPATIALLY HOMOGENEOUS AND ISOTROPIC EINSTEIN-VLASOV-FOKKER-PLANCK SYSTEM WITH COSMOLOGICAL SCALAR FIELD.
- Authors
Calogero, Simone; Pankavich, Stephen
- Abstract
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.
- Subjects
HOMOGENEOUS spaces; FOKKER-Planck equation; EINSTEIN field equations; ISOTROPIC properties; SCALAR field theory; VLASOV equation
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 5, p1063
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018041