# 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…

## 4 Citations

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

- Mathematics, PhysicsActa Applicandae Mathematicae
- 2022

The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some…

### Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas

- Mathematics
- 2022

,

### Global bounded solutions to the Boltzmann equation for a polyatomic gas

- Mathematics
- 2022

. 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

- Mathematics, Physics
- 2022

The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some…

### On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

- MathematicsJournal of Mathematical Physics
- 2023

In the present article, 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

- Physics
- 1988

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

- Mathematics
- 2012

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

- Mathematics31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31
- 2019

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

- Mathematics
- 2010

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

- Mathematics, Physics
- 1975

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.

### On the equivalence between the probabilistic, kinetic, and scattering kernel formulations of the Boltzmann equation

- Physics, Computer Science
- 1990

### Functional Analysis I

- Mathematics
- 2017

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…