Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

Classical solutions for fractional porous medium flow

(2021) Young-Pil Choi et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Critical thresholds in one dimensional damped Euler-Poisson systems

(2020) Manas Bhatnagar et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces

(2020) José A. Carrillo et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles

(2020) J.A. Carrillo et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Mean field limit for Coulomb-type flows

(2020) Sylvia Serfaty   DUKE MATHEMATICAL JOURNAL

Quantifying the Hydrodynamic Limit of Vlasov-Type Equations with Alignment and Nonlocal Forces

(2020) Jose A. Carrillo et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model

(2019) Didier Bresch et al.   COMPTES RENDUS MATHEMATIQUE

Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞ kernels

(2018) Pierre-Emmanuel Jabin et al.   INVENTIONES MATHEMATICAE

Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones

(2018) Young-Pil Choi et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Mean-field limit for collective behavior models with sharp sensitivity regions

(2018) José Carrillo et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Convergence to Equilibrium in Wasserstein Distance for Damped Euler Equations with Interaction Forces

(2018) José A. Carrillo et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

(2018) Young-Pil Choi et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

A rigorous derivation from the kinetic Cucker–Smale model to the pressureless Euler system with nonlocal alignment

(2018) Alessio Figalli et al.   Analysis & PDE

Weak solutions for Euler systems with non-local interactions

(2017) José A. Carrillo et al.   JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

Single to double mill small noise transition via semi-Lagrangian finite volume methods

(2016) José A. Carrillo et al.   Communications in Mathematical Sciences

From gas dynamics with large friction to gradient flows describing diffusion theories

(2016) Corrado Lattanzio et al.   COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

The Cauchy problem for the pressureless Euler/isentropic Navier–Stokes equations

(2016) Young-Pil Choi et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Mean field limit and propagation of chaos for Vlasov systems with bounded forces

(2016) Pierre-Emmanuel Jabin et al.   JOURNAL OF FUNCTIONAL ANALYSIS

On the pressureless damped Euler–Poisson equations with quadratic confinement: Critical thresholds and large-time behavior

(2016) José A. Carrillo et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

First-order aggregation models with alignment

(2016) Razvan C. Fetecau et al.   PHYSICA D-NONLINEAR PHENOMENA

Mean-Field Limits for Some Riesz Interaction Gradient Flows

(2016) Mitia Duerinckx   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Particle approximation of Vlasov equations with singular forces: Propagation of chaos

(2015) Maxime Hauray et al.   ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE

First-order aggregation models and zero inertia limits

(2015) R.C. Fetecau et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS

(2015) Mircea Petrache et al.   Journal of the Institute of Mathematics of Jussieu

Hydrodynamic limit of the kinetic Cucker–Smale flocking model

(2015) Trygve K. Karper et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Propagation of chaos for the 2D viscous vortex model

(2014) Nicolas Fournier et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

A simple proof of the Cucker-Smale flocking dynamics and mean-field limit

(2013) Seung-Yeal Ha et al.   Communications in Mathematical Sciences

Relative Entropy in Diffusive Relaxation

(2013) Corrado Lattanzio et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Nonlocal interactions by repulsive–attractive potentials: Radial ins/stability

(2012) D. Balagué et al.   PHYSICA D-NONLINEAR PHENOMENA

Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations

(2011) J. A. Carrillo et al.   DUKE MATHEMATICAL JOURNAL

From particle to kinetic and hydrodynamic descriptions of flocking

(2011) Eitan Tadmor et al.   Kinetic and Related Models

STOCHASTIC MEAN-FIELD LIMIT: NON-LIPSCHITZ FORCES AND SWARMING

(2011) FRANÇOIS BOLLEY et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE

(2010) JOSÉ A. CARRILLO et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

On the global regularity of subcritical Euler–Poisson equations with pressure

(2009) Eitan Tadmor et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Double milling in self-propelled swarms from kinetic theory

(2009) José Carrillo et al.   Kinetic and Related Models

WASSERSTEIN DISTANCES FOR VORTICES APPROXIMATION OF EULER-TYPE EQUATIONS

(2009) MAXIME HAURAY   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES