Proof of spherical flocking based on quantitative rearrangement inequalities

DOI10.2422/2036-2145.201909_007zbMath1478.49020arXiv1909.04595OpenAlexW3126432538MaRDI QIDQ5161612

Rupert L. Frank, Elliott H. Lieb

Publication date: 1 November 2021

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04595

zbMATH Keywords

flocking modelRiesz-Sobolev inequalityquadratic rearrangement inequality

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Estimates of eigenvalues in context of PDEs (35P15)

Related Items

Inequalities of Riesz-Sobolev type for compact connected abelian groups ⋮ Classifying Minimum Energy States for Interacting Particles: Spherical Shells ⋮ Some minimization problems for mean field models with competing forces ⋮ Rigidity for measurable sets ⋮ A note on some non-local variational problems ⋮ Nonlocal energies of convex bodies and their log-Minkowski problems ⋮ Classifying minimum energy states for interacting particles: regular simplices ⋮ From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials ⋮ A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem ⋮ Sharp stability for the interaction energy

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