{"paper":{"title":"Preventing $L^p$ blow-up by local anisotropy of signal production in the Keller-Segel system with strongly differing diffusion rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Youshan Tao","submitted_at":"2026-06-04T10:59:51Z","abstract_excerpt":"In a smoothly bounded domain $\\Omega\\subset R^n$, $n\\le 5$, the manuscript considers the variant of the Keller-Segel system given by \\[\n  \\left\\{ \\begin{array}{l} \n  u_t = D \\Delta u - \\nabla \\cdot (u\\nabla v), \\\\[1mm]\n  v_t = d \\Delta v + \\nabla \\cdot (u\\nabla v) - v + u,\n  \\end{array} \\right. \\] which involves an additional contribution $\\nabla \\cdot (u\\nabla v)$ to the chemoattractant evolution, in line with refined modeling literature reflecting an anisotropic correction to the isotropic signal production term $+u$ in the classical Keller-Segel model.\n  It is shown that for arbitrary $D>0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06009","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/2606.06009/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"}