### Abstract

Original language | English |
---|---|

Article number | 14450 |

Pages (from-to) | 137-177 |

Number of pages | 41 |

Journal | Kinetic and Related Models |

Volume | 11 |

Issue number | 1 |

Early online date | 16 Aug 2017 |

DOIs | |

Publication status | Published - 1 Feb 2018 |

### Fingerprint

### Keywords

- math.AP
- math-ph
- math.MP
- Derivation
- Boltzmann equation
- Semigroups
- Rayleigh gas

### Cite this

*Kinetic and Related Models*,

*11*(1), 137-177. [14450]. https://doi.org/10.3934/krm.2018008

**The derivation of the linear Boltzmann equation from a Rayleigh gas particle model.** / Matthies, Karsten; Stone, George Russell; Theil, Florian.

Research output: Contribution to journal › Article

*Kinetic and Related Models*, vol. 11, no. 1, 14450, pp. 137-177. https://doi.org/10.3934/krm.2018008

}

TY - JOUR

T1 - The derivation of the linear Boltzmann equation from a Rayleigh gas particle model

AU - Matthies, Karsten

AU - Stone, George Russell

AU - Theil, Florian

PY - 2018/2/1

Y1 - 2018/2/1

N2 - A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background particles, which do not interact among each other. In the Boltzmann-Grad scaling, we derive the validity of a linear Boltzmann equation for arbitrary long times under moderate assumptions on higher moments of the initial distributions of the tagged particle and the possibly non-equilibrium distribution of the background. The convergence of the empiric dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for associated probability measures on collision histories.

AB - A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background particles, which do not interact among each other. In the Boltzmann-Grad scaling, we derive the validity of a linear Boltzmann equation for arbitrary long times under moderate assumptions on higher moments of the initial distributions of the tagged particle and the possibly non-equilibrium distribution of the background. The convergence of the empiric dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for associated probability measures on collision histories.

KW - math.AP

KW - math-ph

KW - math.MP

KW - Derivation

KW - Boltzmann equation

KW - Semigroups

KW - Rayleigh gas

U2 - 10.3934/krm.2018008

DO - 10.3934/krm.2018008

M3 - Article

VL - 11

SP - 137

EP - 177

JO - Kinetic and Related Models

JF - Kinetic and Related Models

SN - 1937-5093

IS - 1

M1 - 14450

ER -