Ellipsoidal BGK model (ES-BGK) is a generalized version of the Boltzmann-BGK model.
In this model, the local Maxwellian in the relaxation operator is extended to an ellipsoidal Gaussian
with a Prandtl parameter ν, so that the correct Prandtl number can be computed in the Navier-Stokes
limit. In this talk, we review some of the recent results on ES-BGK model, such as the existence
(stationary or non-stationary) theory and the entropy-entropy production estimates. A dichotomy
is observed between −1/2 < v < 1 and ν=−1/2. In the former case, an equivalence relation between
the local temperature and the temperature tensor enables one to apply theories developed
for the original BGK model in a modified form. In the critical case (ν=−1/2), where the correct
Prandtl number is achieved, such equivalence breaks down, and the structure of the flow has
to be incorporated to estimate the temperature tensor from below. This is from joint works with
Stephane Brull, Doheon Kim, and Son Sung Jun.
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