Relaxation-time model for the post-Newtonian Boltzmann equation

Variational formula for the relaxation time in the Boltzmann equation.

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the...

Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data. Unique global-in-time mild solutions are obtained uniformly in the speed of light parameter c ≥ 1. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as c→∞ on arbitrary time intervals [0, T ], with conv...

The Newtonian limit of the relativistic Boltzmann equation

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter c>c0 for a properly large and positive c0. A local existence and uniqueness theorem is proved in an interval of time independent of c>c0 and conditions are given such that in the limit c→+∞ the solutions converge, in a suita...

Single relaxation time model for entropic lattice Boltzmann methods.

For lattice Boltzmann methods based on entropy functions, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. Implementation of the two-dimensional hydrodynamics demonstrates considerable increase of stability with respect to conventional lattice Boltzmann schemes.

Equilibration Rate for the Linear Inhomogeneous Relaxation-time Boltzmann Equation for Charged