• Corpus ID: 245704613

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

@inproceedings{Bernhoff2022LinearizedBC,
  title={Linearized Boltzmann Collision Operator: II. Polyatomic Molecules Modeled by a Continuous Internal Energy Variable},
  author={Niclas Bernhoff},
  year={2022}
}
: The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for mixtures and polyatomic single species where the polyatomicity is modeled by a discrete internal energy variable, are more recently obtained. In this work the compactness of the… 
3 Citations

Figures from this paper

Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures

Abstract: The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral

Global bounded solutions to the Boltzmann equation for a polyatomic gas

. In this paper we consider the Boltzmann equation modelling the motion of a poly- atomic gas where the integration collision operator in comparison with the classical one involves an additional

References

SHOWING 1-10 OF 20 REFERENCES

Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures

Abstract: The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral

On the Cauchy problem for Boltzmann equation modelling a polyatomic gas

In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish

The Boltzmann equation and its applications

I. Basic Principles of The Kinetic Theory of Gases.- 1. Introduction.- 2. Probability.- 3. Phase space and Liouville's theorem.- 4. Hard spheres and rigid walls. Mean free path.- 5. Scattering of a

Diffusion asymptotics of a kinetic model for gaseous mixtures

In this work, we investigate the asymptotic behaviour of the solutions to the non-reactive fully elastic Boltzmann equations for mixtures in the diffusive scaling. We deal with cross sections such as

On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases

In this paper, we propose a formal derivation of the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic gases. We use a direct extension of the model devised in [ 8 , 16 ] for

Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels

We prove an $L^p$ compactness result for the gain parts of the linearized Boltzmann collision operator associated with weakly cutoff collision kernels that derive from a power-law intermolecular

The Linearized Boltzmann Collision Operator for Cut-Off Potentials

Boundedness and compactness of integral operators arising from the linearized Boltzmann collision operator are investigated for a wide class of angular and radial cut-off potentials.

Functional Analysis I

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with