Quantitative fluid approximation in transport theory: a unified approach

DOI10.2140/pmp.2022.3.491OpenAlexW3102080005MaRDI QIDQ2693721

Emeric Bouin, Clément Mouhot

Publication date: 24 March 2023

Published in: Probability and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.07836

zbMATH Keywords

spectral theoryscattering operatoranomalous diffusionkinetic theorytransport processFokker-Planck operatorLévy-Fokker-Planck operator

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) PDEs in connection with fluid mechanics (35Q35) Brownian motion (60J65) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Scattering theory for PDEs (35P25) Fractional derivatives and integrals (26A33) Transport processes in time-dependent statistical mechanics (82C70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Statistical mechanics of gases (82D05) Linear integral equations (45A05) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Fokker-Planck equations (35Q84) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)

Related Items (3)

On a structure-preserving numerical method for fractional Fokker-Planck equations ⋮ Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension ⋮ Quantitative De Giorgi methods in kinetic theory for non-local operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity theory for general stable operators
• Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
• Functional inequalities for stable-like Dirichlet forms
• Fast diffusion equations: matching large time asymptotics by relative entropy methods
• Anomalous transport of particles in plasma physics
• Fractional diffusion limit for collisional kinetic equations
• The fractional diffusion limit of a kinetic model with biochemical pathway
• Hardy-Poincaré inequalities and applications to nonlinear diffusions
• Kinetic derivation of fractional Stokes and Stokes-Fourier systems
• Asymptotics of the fast diffusion equation via entropy estimates
• Limit theorems for additive functionals of a Markov chain
• Anomalous diffusion limit induced on a kinetic equation
• Linear Boltzmann equation and fractional diffusion
• Diffusion approximation for Fokker Planck with heavy tail equilibria: a spectral method in dimension 1
• Anomalous diffusion limit of kinetic equations in spatially bounded domains
• The first and second fluid approximation to the linearized Boltzmann equation
• Kato's inequality when \(\Delta u\) is a measure
• Fractional diffusion limit for a kinetic equation with an interface
• Anomalous diffusion for multi-dimensional critical kinetic Fokker-Planck equations
• Semilinear fractional elliptic equations with gradient nonlinearity involving measures
• Fractional diffusion limit of a kinetic equation with diffusive boundary conditions in the upper-half space
• Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: the critical case
• Superdiffusion of energy in a chain of harmonic oscillators with noise
• Fractional Laplacians : a short survey
• Ballistic and superdiffusive scales in the macroscopic evolution of a chain of oscillators
• Anomalous diffusion limit for a linear Boltzmann equation with external force field
• Fractional diffusion limit for collisional kinetic equations: A moments method
• The Diffusion Limit of Free Molecular Flow in Thin Plane Channels
• One-Parameter Semigroups for Linear Evolution Equations
• Fractional Diffusion Limit for a Fractional Vlasov--Fokker--Planck Equation
• Diffusion limit of Fokker−Planck equation with heavy tail equilibria

This page was built for publication: Quantitative fluid approximation in transport theory: a unified approach