Integrability Propagation for a Boltzmann System Describing Polyatomic Gas Mixtures

.This paper explores the \(Lᵖ\) Lebesgue's integrability propagation, \(p∈ (1,∞ ]\), of a system of space homogeneous Boltzmann equations modelling a multicomponent mixture of polyatomic gases based on the continuous internal energy. For typical collision kernels proposed in the literature, \(L^p\) moment-entropy-based estimates for the collision operator gain part and a lower bound for the loss part are performed, leading to a vector valued inequality for the collision operator and, consequently, to a differential inequality for the vector valued solutions of the system. This allows one to prove the propagation property of the polynomially weighted \(L^p\) norms associated to the vector valued solution of the system of Boltzmann equations. The case \(p=∞\) is found as a limit of the case \(p< ∞\).