Integrability Propagation for a Boltzmann System Describing Polyatomic Gas Mixtures

SIAM Journal on Mathematical Analysis, vol. 56, pp. 1459–1494

Abstract

Abstract. This paper explores the [Formula: see text] Lebesgue’s integrability propagation, [Formula: see text], 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, [Formula: see text] 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 [Formula: see text] norms associated to the vector valued solution of the system of Boltzmann equations. The case [Formula: see text] is found as a limit of the case [Formula: see text].

Authors 2

1. Ricardo J. Alonso

   Texas A&M University · Texas A&M University at Qatar

   Affiliation as printed

   Division of Arts & Sciences, Texas A&M, Education City, Doha, Qatar

2. Milana Pavić‐Čolić Aachen Department of Mathematics and Informatics Faculty of Sciences, University of Novi Sad

   RWTH Aachen University · University of Novi Sad

   Affiliation as printed

   Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia and Applied and Computational Mathematics, RWTH Aachen University, Schinkelstrasse 2, 52062, Aachen, Germany