Global existence and stability of nearly aligned flocks

DOI10.1007/s10884-018-9693-8zbMath1426.92094arXiv1802.08926OpenAlexW2952069428WikidataQ129436627 ScholiaQ129436627MaRDI QIDQ2333300

Roman Shvydkoy

Publication date: 12 November 2019

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.08926

zbMATH Keywords

alignmentflockingfractional LaplacianCucker-Smale

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Animal behavior (92D50)

Related Items (18)

Global solutions to multi-dimensional topological Euler alignment systems ⋮ Swarming: hydrodynamic alignment with pressure ⋮ Global Existence and Limiting Behavior of Unidirectional Flocks for the Fractional Euler Alignment System ⋮ Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment ⋮ Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment ⋮ Finite- and infinite-time cluster formation for alignment dynamics on the real line ⋮ On the Euler-alignment system with weakly singular communication weights ⋮ Singular Cucker–Smale Dynamics ⋮ Topologically Based Fractional Diffusion and Emergent Dynamics with Short-Range Interactions ⋮ Regular solutions to the fractional Euler alignment system in the Besov spaces framework ⋮ On Cucker–Smale dynamical systems with degenerate communication ⋮ Weak and strong solutions to the forced fractional Euler alignment system ⋮ Global regularity for a 1D Euler-alignment system with misalignment ⋮ Density-induced consensus protocol ⋮ Flocking with short-range interactions ⋮ Flocking hydrodynamics with external potentials ⋮ Eulerian Dynamics in Multidimensions with Radial Symmetry ⋮ On the Lagrangian trajectories for the one-dimensional Euler alignment model without vacuum velocity

Cites Work

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• Uniformly attracting limit sets for the critically dissipative SQG equation
• A hydrodynamic model for the interaction of Cucker–Smale particles and incompressible fluid
• Heterophilious Dynamics Enhances Consensus
• Eulerian dynamics with a commutator forcing
• Emergent Behavior in Flocks

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