Hilbert Expansion from the Boltzmann equation to relativistic Fluids

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.

50 pages

References in corpus (3)

• The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Coordinates in the relativistic Boltzmann theory

Cited by in corpus (3)

• Recent developments in mathematical aspects of relativistic fluids
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory