Hilbert Expansion from the Boltzmann equation to relativistic Fluids

Details Hilbert Expansion from the Boltzmann equation to relativistic Fluids Hilbert Expansion from the Boltzmann equation to relativistic Fluids

2010-09-25

arxiv.org/abs/1009.5033v1

Comm. Math. Phys. (2010)

Mathematics

Analysis of PDEs

50 pages

Scientific paper

10.1007/s00220-011-1207-z

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.

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