{"paper":{"title":"A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: Global solvability for large nonradial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit, Michael Winkler","submitted_at":"2017-01-25T17:32:44Z","abstract_excerpt":"The chemotaxis system \\[ \\left\\{ \\begin{array}{l} u_t = \\Delta u - \\chi\\nabla \\cdot (\\frac{u}{v}\\nabla v), v_t=\\Delta v - v+u, \\end{array} \\right. \\] is considered in a bounded domain $\\Omega\\subset \\mathbb{R}^n$ with smooth boundary, where $\\chi>0$. An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter $\\chi$ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that\\[ \\chi < \\left\\{ \\begin{array}{ll} \\infty \\qquad & \\mbox{if } n=2, \\sqrt{8} \\qquad & \\mbo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07391","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"}