Linearized Boltzmann Collision Operator: II. Polyatomic Molecules Modeled by a Continuous Internal Energy Variable

Abstract

The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently, been extended to multi-component mixtures and polyatomic single species with the polyatomicity modeled by a discrete internal energy variable. In this work we prove compactness of the integral operator for polyatomic single species, with the polyatomicity modeled by a continuous internal energy variable, and the number of internal degrees of freedom greater or equal to two. The terms of the integral operator are shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators. Self-adjointness of the linearized collision operator follows. Coercivity of the collision frequency are shown for hard-sphere like and hard potential with cut-off like models, implying Fredholmness of the linearized collision operator.

28 pages, 2 figures

References in corpus (3)

• Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures
• On the Cauchy problem for Boltzmann equation modelling a polyatomic gas
• Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions

Cited by in corpus (5)

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• Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions
• Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas
• Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions
• Linearized Boltzmann collision operator for a mixture of monatomic and polyatomic chemically reacting species