Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].
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 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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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Future global stability of Maxwell-J\"uttner equilibria and vacuum for the massless Boltzmann equation on FLRW spacetimes
Proves future global stability and explicit decay rates for small perturbations of Maxwell-Jüttner equilibria (and vacuum for q > 1/3) of the massless Boltzmann equation on FLRW backgrounds with scale factor t^q, q in [0,1].