Fredholm Property of the Linearized Boltzmann Operator for a Polyatomic Single Gas Model

2022/08/30 by Brull, Stéphane, Shahine, Marwa, Thieullen, Philippe · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.14343

Abstract

In the following work, we consider the Boltzmann equation that models a polyatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section B, we prove that the linearized Boltzmann operator L of this model is a Fredholm operator. For this, we write L as a perturbation of the collision frequency multiplication operator, and we prove that the perturbation operator K is compact. The result is established after inspecting the kernel form of K and proving it to be L² integrable over its domain using elementary arguments.

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• Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions
• Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow
• The half-space problem of evaporation and condensation for polyatomic gases and entropy inequalities

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