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Hilbert expansion from the Boltzmann equation to relativistic fluids. (English) Zbl 1221.35271

The local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion is under consideration. The existence of local solutions to the relativistic Boltzmann equation is proved as they are nearby the local relativistic Maxwellians. The last ones are constructed from a class of solutions to the relativstic Euler equations. This class includes a large subclass of near-constant, non-vacuum fluid states. For small Knudsen number, these solutions to the relativistic Boltzmann equation have dyamics that are effectively captured by corresponding solutions to the relativistic Euler equations.

MSC:

35Q20 Boltzmann equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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