On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field

Simone Calogero; Stephen Pankavich

doi:10.3934/krm.2018041

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2018, Volume 11, Issue 5: 1063-1083. Doi: 10.3934/krm.2018041

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On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field

Simone Calogero^1, and
Stephen Pankavich^2, ,

1.
Department of Mathematics, Chalmers Institute of Technology, University of Gothenburg, Gothenburg, Sweden
2.
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, USA

* Corresponding author: S. Pankavich
* Corresponding author: S. Pankavich

Received: December 2016

Revised: September 2017

Published: May 2018

The second author is supported by the US National Science Foundation under awards DMS-1211667 and DMS-1614586.

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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.

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Mathematics Subject Classification: Primary: 35Q83, 83F05; Secondary: 35Q76, 83C05.

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References

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