Integrability Propagation for a Boltzmann System Describing Polyatomic Gas Mixtures

. This paper explores the \ (L^p\) 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, \ (Lᵖ\) 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 \ (Lᵖ\) 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 \). Keywordsmulticomponent gas mixtures system of Boltzmann equations entropy-based estimatesintegrability propagationMSC codes35Q2076P0582C40