{"paper":{"title":"A Keller-Segel-fluid system with singular sensitivity: Generalized solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit, Masaaki Mizukami, Tobias Black","submitted_at":"2018-05-23T12:18:11Z","abstract_excerpt":"In bounded smooth domains $\\Omega\\subset\\mathbb{R}^N$, $N\\in\\{2,3\\}$, we consider the Keller-Segel-Stokes system \\begin{align*}\n  n_t + u\\cdot \\nabla n &= \\Delta n - \\chi \\nabla \\cdot(\\frac{n}{c}\\nabla c),\\\\ c_t + u\\cdot \\nabla c &= \\Delta c - c + n,\\\\ u_t &= \\Delta u + \\nabla P + n\\nabla \\phi, \\qquad \\nabla \\cdot u=0, \\end{align*} and prove global existence of generalized solutions if \\[\n  \\chi<\\begin{cases}\n  \\infty,&N=2,\\\\ \\frac{5}{3},&N=3.\n  \\end{cases} \\] These solutions are such that blow-up into a persistent Dirac-type singularity is excluded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09085","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"}