# On the Boltzmann equation

@article{Arkeryd1972OnTB,
title={On the Boltzmann equation},
author={L. Arkeryd},
journal={Archive for Rational Mechanics and Analysis},
year={1972},
volume={45},
pages={1-16}
}
• L. Arkeryd
• Published 1972
• Physics, Mathematics
• Archive for Rational Mechanics and Analysis
193 Citations
The homogeneous Boltzmann-Nordheim equation for bosons: existence and uniqueness
The Boltzmann-Nordheim equation is a modification, based on physical considerations, of the Boltzmann equation that describes the dynamics of the distribution of particles in a quantum gas composedExpand
Modélisation mathématique et étude numérique d'un aérosol dans un gaz raréfié. Application à la simulation du transport de particules de poussière en cas d'accident de perte de vide dans ITER.
Dans ce travail, nous nous interessons a des modeles cinetiques decrivant un aerosol constitue de particules solides dans un gaz rarefie. Ces modeles sont constitues d'un couplage de deux EquationsExpand
Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation
• Physics, Mathematics
• 2007
For the spatially homogeneous Boltzmann equation with cutoff hard potentials, it is shown that solutions remain bounded from above uniformly in time by a Maxwellian distribution, provided the initialExpand
On a quantum boltzmann equation for a gas of photons
• Physics
• 2001
Abstract We prove existence and uniqueness of the solution of a homogeneous quantum Boltzmann equation describing the photon–electron interaction. We study the asymptotic behaviour of the solutions,Expand
On the dynamics of finite temperature trapped Bose gases
• Mathematics, Physics
• 2016
The system that describes the dynamics of a Bose-Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB)Expand
Spatially Homogeneous Boltzmann Equation for Relativistic Particles
• Physics, Computer Science
• SIAM J. Math. Anal.
• 2014
The relativistic version of the Povzner inequality is derived and this is used to study the Cauchy problem and investigate how the polynomial and exponential moments in L 1 are propagated. Expand
On measure solutions of the Boltzmann equation, part I: Moment production and stability estimates
• Mathematics
• 2012
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions},Expand
Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particle Bath
• Physics, Mathematics
• 2008
We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host medium with a fixed distribution. This is achieved by controllingExpand
Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem
• Mathematics, Physics
• 2006
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitutionExpand
Stability and Uniqueness for the Spatially Homogeneous Boltzmann Equation with Long-Range Interactions
• Mathematics, Physics
• 2006
In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering all physical collisionExpand

#### References

SHOWING 1-5 OF 5 REFERENCES
On Boltzmann's equation in the kinetic theory of gases
1. Boltzmann's differentio-integral equation for the molecular velocity distribution function in a perfect gas forms the natural starting-point for a mathematical treatment of the kinetic theory ofExpand