Anderson-Witting model is a relaxational model equation of the relativistic Boltzmann equation, which sees a wide application in physics. In this paper, we study the existence of classical solutions and its asymptotic behavior when the solution starts sufficiently close to a global relativistic Maxwellian.

Anderson-Witting model of the relativistic Boltzmann equation near equilibrium

In this paper, the global existence of weak solutions to the relativistic BGK model for the relativistic Boltzmann equation is analyzed. The proof relies on the strong compactness of the de...

Global weak solutions to the relativistic BGK equation

Maxwellian iteration of a causal relativistic model of polyatomic gases and evaluation of bulk, shear viscosity and heat conductivity

Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting model and Marle this http URL this paper, we prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.

On a relativistic BGK model for polyatomic gases near equilibrium

In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These polynomial and exponential $$L^\infty $$
 bounds have been known to be a challenging open problem in relativistic kinetic theory. To accomplish this, we establish two types of estimates for the gain part of the collision operator. First, we prove a potential type estimate and a relativistic hyper-surface integral estimate. We then combine those estimates using the relativistic counterpart of the Carleman representation to derive uniform control of the gain term for the relativistic collision operator. This allows us to prove the desired propagation of the uniform bounds of the solution. We further present two applications of the propagation of the uniform upper bounds: another proof of the Boltzmann H-theorem, and the asymptotic convergence of solutions to the relativistic Maxwellian equilibrium.

Propagation of Uniform Upper Bounds for the Spatially Homogeneous Relativistic Boltzmann Equation

In this paper, we are concerned with the boundary value problem in a slab for the stationary relativistic BGK model of Marle type, which is a relaxation model of the relativistic Boltzmann equation. In the case of fixed inflow boundary conditions, we establish the existence of unique stationary solutions.

Stationary solutions to the boundary value problem for the relativistic BGK model in a slab

Stationary solutions to the boundary value problem for relativistic BGK model in a slab

The Anderson--Witting model is a relativistic generalization of the Bhatnagar--Gross--Krook model which is well-known as the relaxation-time approximation of the celebrated Boltzmann equation. In t...

Byung-Hoon Hwang

Papers

Stationary solutions to the boundary value problem for the relativistic BGK model in a slab

Anderson-Witting model of the relativistic Boltzmann equation near equilibrium

Stationary solutions to the boundary value problem for relativistic BGK model in a slab

Stationary Solutions to the Anderson--Witting Model of the Relativistic Boltzmann Equation in a Bounded Interval

On a relativistic BGK model for polyatomic gases near equilibrium