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Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions. (English) Zbl 1497.76076

Summary: In this paper, we investigate a compactness property of the linearized Boltzmann operator in the context of a polyatomic gas whose molecules undergo resonant collisions. The peculiar structure of resonant collision rules allows to tensorize the problem into a velocity-related one, neighbouring the monatomic case, and an internal energy-related one. Our analysis is based on a specific treatment of the internal energy contributions. We also propose a geometric variant of Grad’s proof of the same compactness property in the monatomic case.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q20 Boltzmann equations
35Q35 PDEs in connection with fluid mechanics
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