{"paper":{"title":"Sublinear signal production in a two-dimensional Keller-Segel-Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2016-02-01T11:32:38Z","abstract_excerpt":"We study the chemotaxis-fluid system \\begin{align*} \\left\\{\\begin{array}{r@{\\,}l@{\\quad}l@{\\,}c} n_{t}&=\\Delta n-\\nabla\\!\\cdot(n\\nabla c)-u\\cdot\\!\\nabla n,\\ &x\\in\\Omega,& t>0,\\\\ c_{t}&=\\Delta c-c+f(n)-u\\cdot\\!\\nabla c,\\ &x\\in\\Omega,& t>0,\\\\ u_{t}&=\\Delta u+\\nabla P+n\\cdot\\!\\nabla\\phi,\\ &x\\in\\Omega,& t>0,\\\\ \\nabla\\cdot u&=0,\\ &x\\in\\Omega,& t>0, \\end{array}\\right. \\end{align*} where $\\Omega\\subset\\mathbb{R}^2$ is a bounded and convex domain with smooth boundary, $\\phi\\in W^{1,\\infty}\\left(\\Omega\\right)$ and $f\\in C^1([0,\\infty))$ satisfies $0\\leq f(s)\\leq K_0 s^\\alpha$ for all $s\\in[0,\\infty)$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00480","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"}