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Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids

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Abstract

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 Maxwellians. The Maxwellians are 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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Authors and Affiliations

  1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom

    Jared Speck

  2. Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA, 19104-6395, USA

    Robert M. Strain

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  1. Jared Speck
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  2. Robert M. Strain
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Correspondence to Robert M. Strain.

Additional information

Communicated by P. Constantin

J.S. was supported by the Commission of the European Communities, ERC Grant Agreement No 208007.

R.M.S. was supported in part by the NSF grant DMS-0901463.

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Speck, J., Strain, R.M. Hilbert Expansion from the Boltzmann Equation to Relativistic Fluids. Commun. Math. Phys. 304, 229–280 (2011). https://doi.org/10.1007/s00220-011-1207-z

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