{"paper":{"title":"Uniqueness of the stochastic Keller-Segel model in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Debopriya Mukherjee, Erika Hausenblas, Thanh Tran","submitted_at":"2022-09-27T06:44:06Z","abstract_excerpt":"In a recent paper (J. Differential Equations, 310: 506-554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak-Keller-Segel system in 1 dimension (1D), driven by time-homogeneous spatial Wiener processes. The current paper is a continuation and consists of two results about the stochastic Patlak-Keller-Segel system in 1D. First, we establish some additional regularity results of the solutions. The additional regularity is, e.g. important for its numerical modeling. Then, as a second result, we obtain the pathwise uniqueness of the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13188","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/2209.13188/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"}