Gain of regularity for the relativistic collision operator

DOI10.1016/j.aml.2018.11.001zbMath1408.81034arXiv1808.10147OpenAlexW2889074119WikidataQ128958940 ScholiaQ128958940MaRDI QIDQ1726604

Jin Woo Jang, Seok-Bae Yun

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.10147

zbMATH Keywords

Boltzmann equationspecial relativitycollision operatorregularizing effectangular cut-off

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) (S)-matrix theory, etc. in quantum theory (81U20) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Equations and inequalities involving linear operators, with vector unknowns (47A50) Boltzmann equations (35Q20)

Related Items (10)

An introduction to the relativistic kinetic theory on curved spacetimes ⋮ On a Relativistic BGK Model for Polyatomic Gases Near Equilibrium ⋮ Propagation of \(L^p\) estimates for the spatially homogeneous relativistic Boltzmann equation ⋮ Stationary Solutions to the Anderson--Witting Model of the Relativistic Boltzmann Equation in a Bounded Interval ⋮ The relativistic quantum Boltzmann equation near equilibrium ⋮ Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation ⋮ Global existence of bounded solutions to the relativistic BGK model ⋮ Asymptotic stability of the relativistic Boltzmann equation without angular cut-off ⋮ Anderson-Witting model of the relativistic Boltzmann equation near equilibrium ⋮ The spatially homogeneous Boltzmann equation for massless particles in an FLRW background

Cites Work

• Coordinates in the relativistic Boltzmann theory
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• A direct method for the regularity of the gain term in the Boltzmann equation
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• The geometry of binary collisions and generalized Radon transforms
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials
• Asymptotic stability of the relativistic Maxwellian
• Smoothing Property of the Gain Term of the Boltzmann Collision Operator
• Regularity in the boltzmann equation and the radon transform
• Regularity of the Gain Term and Strong $L^1 $ Convergence to Equilibrium for the Relativistic Boltzmann Equation

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