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In this paper, we establish the entropy-entropy production estimate for theES-BGK model, a generalized version of the BGK model of the Boltzmann equationintroduced for better approximation in the Navier-Stokes limit. Our resultimproves the previous entropy production estimate [39] in that (1) the fullrange of Prandtl parameters $-1/2\leq\nu <1$ including the critical case$\nu=-1/2$ is covered, and (2) a sharper entropy production bound is obtained.An explicit characterization of the coefficient of the entropy-entropyproduction estimate is also presented.

Entropy production estimate for the ES-BGK model with the correct Prandtl number