From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules

DOI10.24033/asens.2318zbMath1371.82086arXiv1510.01123OpenAlexW2962680724MaRDI QIDQ2981854

Arnaud Guillin, Nicolas Fournier

Publication date: 10 May 2017

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01123

zbMATH Keywords

stabilityconvergenceuniquenesswell-posednessBoltzmann equationgrazing collisionsLandau equationpropagation of chaosexistence and regularity of solutionsMaxwellian moleculesKac stochastic particle systemLandau processes

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Weak solutions to PDEs (35D30) Integro-partial differential equations (35R09)

Related Items (17)

Distribution dependent SDEs driven by additive continuous noise ⋮ Kac's process with hard potentials and a moderate angular singularity ⋮ Distribution dependent SDEs for Landau type equations ⋮ A Kac model for kinetic annihilation ⋮ Nonlinear Fokker-Planck equations for probability measures on path space and path-distribution dependent sdes ⋮ Chaos for rescaled measures on Kac's sphere ⋮ High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials ⋮ Construction of Boltzmann and McKean-Vlasov type flows (the sewing lemma approach) ⋮ Poisson Equation on Wasserstein Space and Diffusion Approximations for Multiscale McKean–Vlasov Equation ⋮ High order approximation for the Boltzmann equation without angular cutoff ⋮ Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials ⋮ Quantitative uniform propagation of chaos for Maxwell molecules ⋮ On a thermostated Kac model with rescaling ⋮ Central limit theorem and moderate deviation principle for McKean-Vlasov SDEs ⋮ Bismut formula for Lions derivative of distribution dependent SDEs and applications ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ Harnack inequalities for McKean-Vlasov SDEs driven by subordinate Brownian motions

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