Nov 16 – 19, 2021
Polytech Lille
Europe/Paris timezone

Compactness property of the linearized Boltzmann operator

Nov 17, 2021, 4:15 PM
2h 15m
Salle Pasteur (Polytech Lille)

Salle Pasteur

Polytech Lille


Marwa Shahine (University of Bordeaux)


We consider the Boltzmann equation that models a polyatomic gas by taking into account the continuous microscopic internal energy I. In particular, we consider the kinetic system proposed by [2], which is based on the procedure of Borgnakke and Larsen [1]. We linearize the Boltzmann equation around the Maxwellian function, which represents the equilibrium distribution function. Under some convenient assumptions on the collision cross-section B, we prove that the linearized Boltzmann operator L is a Fredholm operator. For this, we write L as L = K − ν.I, and we prove that K is a compact operator. The compactness is achieved as a result of K being a Hilbert-Schmidt integral operator.
This work was indeed done by Grad [3] for a monoatomic single gas, and by Pavic [4] for a mixture of monoatomic gases.

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