The ellipsoidal-Bhatnagar, Gross, and Krook (ES-BGK) model is introduced as a generalized version of the original BGK model with the aim of calculating the correct Prandtl number, which is the ratio between viscosity and thermal conductivity. In this paper, we study the existence and uniqueness of Lp-solutions to the ES-BGK model for the polyatomic molecules, within the range 1 ≤ p ≤ ∞. This research aims to provide a comprehensive analysis in pursuit of a better understanding of the behavior of these systems.
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