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Zeitschriftenartikel

The Einstein-Boltzmann system and positivity

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons49385

Lee,  Ho
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20696

Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Externe Ressourcen
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Volltexte (frei zugänglich)

1203.2471
(Preprint), 285KB

S0219891613500033.pdf
(beliebiger Volltext), 403KB

Ergänzendes Material (frei zugänglich)
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Zitation

Lee, H., & Rendall, A. D. (2013). The Einstein-Boltzmann system and positivity. Journal of hyperbolic differential equations, 77(1), 77-104. doi:10.1142/S0219891613500033.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-4D9D-D
Zusammenfassung
The Einstein-Boltzmann system is studied, with particular attention to the non-negativity of the solution of the Boltzmann equation. A new parametrization of post-collisional momenta in general relativity is introduced and then used to simplify the conditions on the collision cross-section given by Bancel and Choquet-Bruhat. The non-negativity of solutions of the Boltzmann equation on a given curved spacetime has been studied by Bichteler and by Tadmon. By examining to what extent the results of these authors apply in the framework of Bancel and Choquet-Bruhat, the non-negativity problem for the Einstein-Boltzmann system is resolved for a certain class of scattering kernels. It is emphasized that it is a challenge to extend the existing theory of the Cauchy problem for the Einstein-Boltzmann system so as to include scattering kernels which are physically well-motivated.