Local existence of weak solutions to kinetic Cucker‐Smale‐Fokker‐Planck equation with singular commutation weights

DOI10.1002/mma.9092OpenAlexW4319319801MaRDI QIDQ6184061

Yaxian Ma, Donghao Li, Xian-Wen Zhang

Publication date: 5 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.9092

zbMATH Keywords

existenceweak solutionsflockingkinetic Cucker-Smale-Fokker-Planckvelocity moment

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Weak solutions to PDEs (35D30) Fokker-Planck equations (35Q84)

Cites Work

• On the Cauchy problem of the Vlasov-Poisson-BGK system: global existence of weak solutions
• A kinetic flocking model with diffusion
• Emergent dynamics of Cucker-Smale flocking particles in a random environment
• From particle to kinetic and hydrodynamic descriptions of flocking
• On the mathematics of emergence
• On the Fokker-Planck-Boltzmann equation
• Propagation of moments and regularity for the 3-dimensional Vlasov- Poisson system
• Propagation of space moments in the Vlasov-Poisson equation and further results
• On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
• Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
• Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system
• Regular solutions of the Vlasov-Poisson-Fokker-Planck system.
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Smoothing effect for the nonlinear Vlasov-Poisson-Fokker-Planck system
• On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
• Complete classification of the asymptotical behavior for singular C-S model on the real line
• A probabilistic approach for the mean-field limit to the Cucker-Smale model with a singular communication
• A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
• On the kinetic Fokker-Planck equation in the half-space with absorbing barriers
• Space Moments of the Vlasov--Poisson System: Propagation and Regularity
• A WELL-POSEDNESS THEORY IN MEASURES FOR SOME KINETIC MODELS OF COLLECTIVE MOTION
• Asymptotic Flocking Dynamics for the Kinetic Cucker–Smale Model
• Particle, kinetic, and hydrodynamic models of swarming
• Discrete Cucker--Smale Flocking Model with a Weakly Singular Weight
• Local well-posedness of the generalized Cucker-Smale model with singular kernels
• Global weak solutions of Vlasov‐Maxwell systems
• Global existence for the Vlasov-Poisson/Fokker-Planck equation in many dimensions, for small data
• Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions
• On the classical solutions of the initial value problem for the unmodified non‐linear vlasov equation II special cases
• Long-time behaviour for solutions of the Vlasov-Poisson-Fokker-Planck equation
• Time decy, propagarion of low moments and dispersive
• Existence of Weak Solutions to Kinetic Flocking Models
• Singular Cucker–Smale Dynamics
• Moment Propagation for Weak Solutions to the Vlasov–Poisson System
• The Kinetic Cucker--Smale Model: Well-Posedness and Asymptotic Behavior
• Emergent Behavior in Flocks

This page was built for publication: Local existence of weak solutions to kinetic Cucker‐Smale‐Fokker‐Planck equation with singular commutation weights