Cauchy Theory for General Kinetic Vicsek Models in Collective Dynamics and Mean-Field Limit Approximations

DOI10.1137/21M1405885WikidataQ114074078 ScholiaQ114074078MaRDI QIDQ5037711

Sara Merino-Aceituno, Marc Briant, A. Diez

Publication date: 4 March 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.00883

zbMATH Keywords

well-posednessmean-field limitcollective dynamicsVicsek modelnonlinear Fokker-Planck equation on the spherenormalized interaction kernelsVicsek-Kolmogorov equation

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Weak solutions to PDEs (35D30) General biology and biomathematics (92B05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84) Transport equations (35Q49)

Related Items

Bulk Topological States in a New Collective Dynamics Model ⋮ Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies ⋮ Dynamics of a spatially homogeneous Vicsek model for oriented particles on a plane ⋮ Derivation of the viscoelastic stress in Stokes flows induced by nonspherical Brownian rigid particles through homogenization ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications

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