{"paper":{"title":"On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Charles Collot, Kaiqiang Zhang","submitted_at":"2024-06-17T09:25:18Z","abstract_excerpt":"We consider the parabolic-elliptic Keller-Segel system in spatial dimensions $d\\geq3$, which corresponds to the mass supercritical case. Some solutions become singular in finite time, an important example being backward self-similar solutions. Herrero et al. and Brenner et al. showed the existence of such profiles, countably many in dimensions $3\\leq d \\leq 9$ and at least two for $d\\geq 10$. We establish that all these self-similar profiles are stable along a set of initial data with finite Lipschitz codimension equal to the number of instable eigenmodes. This extends the recent finding of Gl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.11358","kind":"arxiv","version":2},"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/2406.11358/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"}