Sok-Bae Yoon

The BGK model has been widely used in place of the Boltzmann equation because of the qualitatively satisfactory results it provides at relatively low computational cost. There is, however, a major drawback to the BGK model: The hydrodynamic limit at the Navier--Stokes level is not correct. One piece of evidence is that the Prandtl number computed using the BGK model does not agree with what is derived from the Boltzmann equation. To overcome this problem, Holway [Rarefied Gas Dynamics, Vol. 1, A

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform L2-stability for nonlinear perturbations.

The ellipsoidal BGK model (ES-BGK) is a generalized version of the original BGK model, designed to yield the correct Prandtl number in the Navier-Stokeslimit. In this paper, we make two observations on the entropy production functional of the ES-BGK model. First, we show that the Cercignani type estimate holds for the ES-BGK model in the whole range of relaxation parameter $-1/2<\nu<1$.Secondly, we observe that the ellipsoidal relaxation operator satisfies an unexpected sign-definite property.So

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier–Stokes–BGK system consisting of the BGK model of Boltzmann equation and incompressible Navier–Stokes equations coupled through a drag forcing term. This is achieved by combining weak compactness of the particle interaction operator based on Dunford–Pettis theorem, strong compactness of macroscopic fields of the kineti