{"paper":{"title":"Sharp conditions to avoid collisions in singular Cucker-Smale interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Peszek, Jose A. Carrillo, Piotr B. Mucha, Young-Pil Choi","submitted_at":"2016-09-12T15:26:05Z","abstract_excerpt":"We consider the Cucker-Smale flocking model with a singular communication weight $\\psi(s) = s^{-\\alpha}$ with $\\alpha > 0$. We provide a critical value of the exponent $\\alpha$ in the communication weight leading to global regularity of solutions or finite-time collision between particles. For $\\alpha \\geq 1$, we show that there is no collision between particles in finite time if they are placed in different positions initially. For $\\alpha\\geq 2$ we investigate a version of the Cucker-Smale model with expanded singularity i.e. with weight $\\psi_\\delta(s) = (s-\\delta)^{-\\alpha}$, $\\delta\\geq 0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}