On a Positive decomposition of entropy production functional for the polyatomic BGK model

TL;DR

This paper demonstrates that the entropy production functional for the polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts, leading to new insights into the model's properties.

Contribution

It introduces a positive decomposition of the entropy production functional for the polyatomic BGK model, enabling new proofs of the H-theorem and compactness results.

Findings

Entropy production functional can be decomposed into two non-negative parts.

The decomposition facilitates proof of the H-theorem for the model.

Establishes weak compactness of the relaxation operator.

Abstract

In this paper, we show that the entropy production functional for the polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts. Two applications of this property: the $H$-theorem for the polyatomic BGK model and the weak compactness of the polyatomic ellipsoidal relaxation operator, are discussed.