Mean-Field Limits: From Particle Descriptions to Macroscopic Equations

José A. Carrillo, Young-Pil Choi

Type: Article

Publication Date: 2021-06-01

Citations: 25

DOI: https://doi.org/10.1007/s00205-021-01676-x

Abstract

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.

Locations

Archive for Rational Mechanics and Analysis - View - PDF
PubMed Central - View
arXiv (Cornell University) - View - PDF
PubMed - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Large friction limit of pressureless Euler equations with nonlocal forces	2020	Young-Pil Choi
+	Large friction limit of pressureless Euler equations with nonlocal forces	2020	Young-Pil Choi
+ PDF Chat	Large friction limit of pressureless Euler equations with nonlocal forces	2021	Young-Pil Choi
+	Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation	2018	Simone Fagioli Emanuela Radici
+	Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation	2018	Simone Fagioli Emanuela Radici
+ PDF Chat	The Mean-Field Limit for Hybrid Models of Collective Motions with Chemotaxis	2023	Roberto Natalini Thierry Paul
+ PDF Chat	Solutions to aggregation–diffusion equations with nonlinear mobility constructed via a deterministic particle approximation	2018	Simone Fagioli Emanuela Radici
+	Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces	2020	José A. Carrillo Young-Pil Choi Jinwook Jung
+	Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces	2020	José A. Carrillo Young-Pil Choi Jinwook Jung
+	Mean-field limit of collective dynamics with time-varying weights	2022	Nastassia Pouradier Duteil
+	On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions	2017	José A. Carrillo Aneta Wróblewska‐Kamińska Ewelina Zatorska
+	On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions	2017	José A. Carrillo Aneta Wróblewska‐Kamińska
+	Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces	2019	José A. Carrillo Young-Pil Choi
+	Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces	2019	José A. Carrillo Young-Pil Choi
+	Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions	2023	Emiliano Cristiani Nadia Loy Marta Menci Andrea Tosin
+ PDF Chat	On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions	2018	José A. Carrillo Aneta Wróblewska‐Kamińska Ewelina Zatorska
+	Deterministic particle approximation for nonlocal transport equations with nonlinear mobility	2018	Marco Di Francesco Simone Fagioli Emanuela Radici
+	Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces	2020	José A. Carrillo Young-Pil Choi Jinwook Jung
+ PDF Chat	Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming	2024	Nilasis Chaudhuri Young-Pil Choi Oliver Tse Ewelina Zatorska
+ PDF Chat	Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces	2020	José A. Carrillo Young-Pil Choi

Works That Cite This (25)

Action	Title	Year	Authors
+ PDF Chat	On well-posedness and singularity formation for the Euler–Riesz system	2021	Young-Pil Choi In-Jee Jeong
+ PDF Chat	Mean-Field Limit Derivation of a Monokinetic Spray Model with Gyroscopic Effects	2024	Matthieu Ménard
+	Small mass limit in mean field theory for stochastic <i>N</i> particle system	2022	Wei Wang Guangying Lv Jinlong Wei
+ PDF Chat	Relaxation to Fractional Porous Medium Equation from Euler–Riesz System	2021	Young-Pil Choi In-Jee Jeong
+ PDF Chat	From BGK-alignment model to the pressured Euler-alignment system with singular communication weights	2023	Young-Pil Choi Byung-Hoon Hwang
+ PDF Chat	Large friction limit of pressureless Euler equations with nonlocal forces	2021	Young-Pil Choi
+ PDF Chat	Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment	2024	Xiang Bai Linan Li Xiaojing Xu
+	Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population	2022	Daniel A. Messenger Graycen E. Wheeler Xuedong Liu David M. Bortz
+	Local well-posedness for the kinetic Cucker–Smale model with super-Coulombic communication weights	2023	Young-Pil Choi Jinwook Jung
+ PDF Chat	Inevitable monokineticity of strongly singular alignment	2023	M. Fabisiak Jan Peszek

Works Cited by This (68)

Action	Title	Year	Authors
+ PDF Chat	An introduction to the nonlinear boltzmann-vlasov equation	1984	Helmut Neunzert
+ PDF Chat	The derivation of swarming models: Mean-field limit and Wasserstein distances	2014	José A. Carrillo Young-Pil Choi Maxime Hauray
+	Large Scale Dynamics of Interacting Particles	1991	Herbert Spohn
+ PDF Chat	First-order aggregation models and zero inertia limits	2015	Razvan C. Fetecau W. Sun
+ PDF Chat	NEXT ORDER ASYMPTOTICS AND RENORMALIZED ENERGY FOR RIESZ INTERACTIONS	2015	Mircea Petrache Sylvia Serfaty
+ PDF Chat	Mean field limit for the one dimensional Vlasov-Poisson equation	2014	Maxime Hauray
+ PDF Chat	Mean-Field Limits for Some Riesz Interaction Gradient Flows	2016	Mitia Duerinckx
+ PDF Chat	On the Dynamics of Large Particle Systems in the Mean Field Limit	2016	François Golse
+ PDF Chat	Incompressible Euler and E-MHD as scaling limits of the Vlasov-Maxwell system	2003	Yann Brenier Norbert J. Mauser Marjolaine Puel
+	SELF-PROPELLED INTERACTING PARTICLE SYSTEMS WITH ROOSTING FORCE	2010	José A. Carrillo Axel Klar S. Martin Sudarshan Tiwari