{"paper":{"title":"Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2017-05-17T12:49:57Z","abstract_excerpt":"We study the chemotaxis-fluid system \\begin{align*} \\left\\{ \\begin{array}{r@{\\,}c@{\\,}c@{\\ }l@{\\quad}l@{\\quad}l@{\\,}c} n_{t}&+&u\\cdot\\!\\nabla n&=\\Delta n-\\nabla\\!\\cdot(\\frac{n}{c}\\nabla c),\\ &x\\in\\Omega,& t>0, c_{t}&+&u\\cdot\\!\\nabla c&=\\Delta c-nc,\\ &x\\in\\Omega,& t>0, u_{t}&+&\\nabla P&=\\Delta u+n\\nabla\\phi,\\ &x\\in\\Omega,& t>0, &&\\nabla\\cdot u&=0,\\ &x\\in\\Omega,& t>0, \\end{array}\\right. \\end{align*} under homogeneous Neumann boundary conditions for $n$ and $c$ and homogeneous Dirichlet boundary conditions for $u$, where $\\Omega\\subset\\mathbb{R}^2$ is a bounded domain with smooth boundary and $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06131","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"}