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.

arXiv comment50 pages

References in corpus (5)

• The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum
• Coordinates in the relativistic Boltzmann theory
• The Non-relativistic Limit of the Euler Nordström System with Cosmological Constant

Cited by in corpus (11)

• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State
• The Nonlinear Stability of the Trivial Solution to the Maxwell-Born-Infeld System
• Large-Time Decay of the Soft Potential relativistic Boltzmann equation in ${\mathbb{R}}_x^3$
• On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics
• Global Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system
• Recent developments in mathematical aspects of relativistic fluids
• Gapless non-hydrodynamic modes in relativistic kinetic theory
• Anderson-Witting model of the relativistic Boltzmann equation near equilibrium
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state