{"paper":{"title":"Global very weak solutions to a chemotaxis-fluid system with nonlinear diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2017-12-01T10:22:52Z","abstract_excerpt":"We consider the chemotaxis-fluid system \\begin{align}\\label{star}\\tag{$\\diamondsuit$} \\left\\{ \\begin{array}{r@{\\,}c@{\\,}c@{\\ }l@{\\quad}l@{\\quad}l@{\\,}c} n_{t}&+&u\\cdot\\!\\nabla n&=\\Delta n^m-\\nabla\\!\\cdot(n\\nabla c),\\ &x\\in\\Omega,& t>0,\\\\ c_{t}&+&u\\cdot\\!\\nabla c&=\\Delta c-c+n,\\ &x\\in\\Omega,& t>0,\\\\ u_{t}&+&(u\\cdot\\nabla)u&=\\Delta u+\\nabla P+n\\nabla\\phi,\\ &x\\in\\Omega,& t>0,\\\\ &&\\nabla\\cdot u&=0,\\ &x\\in\\Omega,& t>0, \\end{array}\\right. \\end{align} in a bounded domain $\\Omega\\subset\\mathbb{R}^3$ with smooth boundary and $m>1$. Assuming $m>\\frac{4}{3}$ and sufficiently regular nonnegative initial d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00262","kind":"arxiv","version":2},"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"}