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Journal Article

The spatially homogeneous relativistic Boltzmann equation with a hard potential

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

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

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1301.0106
(Preprint), 254KB

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Citation

Lee, H., & Rendall, A. D. (2013). The spatially homogeneous relativistic Boltzmann equation with a hard potential. Communications in Partial Differential Equations, 38(12), 2238-2262. doi:10.1080/03605302.2013.827709.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-77DF-C
Abstract
In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in spatially flat Robertson-Walker spacetimes.