{"paper":{"title":"Singular sensitivity in a Keller-Segel-fluid system","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":"2017-07-18T09:01:51Z","abstract_excerpt":"In bounded smooth domains $\\Omega\\subset\\mathbb{R}^N$, $N\\in\\{2,3\\}$, considering the chemotaxis--fluid system\n  \\[ \\begin{cases} \\begin{split} & 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 + \\kappa (u\\cdot \\nabla) u &= \\Delta u + \\nabla P + n\\nabla \\Phi & \\end{split}\\end{cases} \\] with singular sensitivity, we prove global existence of classical solutions for given $\\Phi\\in C^2(\\bar{\\Omega})$, for $\\kappa=0$ (Stokes-fluid) if $N=3$ and $\\kappa\\in\\{0,1\\}$ (Stokes- or Navier--Stokes fluid) if $N=2$ and unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05528","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"}