{"paper":{"title":"Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler","submitted_at":"2014-10-22T07:39:15Z","abstract_excerpt":"The chemotaxis-Navier-Stokes system linking the chemotaxis equations \\[ n_t + u\\cdot\\nabla n = \\Delta n - \\nabla \\cdot (n\\chi(c)\\nabla c) \\] and \\[ c_t + u\\cdot\\nabla c = \\Delta c-nf(c) \\] to the incompressible Navier-Stokes equations, \\[ u_t + (u\\cdot\\nabla)u = \\Delta u +\\nabla P + n \\nabla \\Phi, \\qquad \\nabla \\cdot u = 0, \\] is considered under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$, in a bounded convex domain $\\Omega\\subset R^3$ with smooth boundary, where $\\Phi\\in W^{1,\\infty}(\\Omega)$, and where $f\\in C^1([0,\\infty))$ and $\\chi\\in C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5929","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"}