{"paper":{"title":"Critical mass for finite-time chemotactic collapse in the critical dimension via comparison","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Meng Liu, Xuan Mao, Yuxiang Li","submitted_at":"2025-05-20T12:29:26Z","abstract_excerpt":"We study the Neumann initial-boundary value problem for the parabolic-elliptic chemotaxis system, proposed by J\\\"ager and Luckhaus (1992). We confirm that their comparison methods can be simplified and refined, applicable to seek the critical mass $8\\pi$ concerning finite-time blowup in the unit disk. As an application, we deal with a parabolic-elliptic-parabolic chemotaxis model involving indirect signal production in the unit ball of $\\mathbb R^4$, proposed by Tao and Winkler (2025). Within the framework of radially symmetric solutions, we prove that if initial mass is less than $64\\pi^2$, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14278","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.14278/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}