{"paper":{"title":"An optimal result for global existence and boundedness in a three-dimensional Keller-Segel-Stokes system with nonlinear diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-07-01T04:24:01Z","abstract_excerpt":"This paper investigates the following quasilinear Keller-Segel-Navier-Stokes system $$\\left\\{\n\\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(n\\nabla c),\\quad x\\in \\Omega, t>0, \\\\ c_t+u\\cdot\\nabla c=\\Delta c-c+n,\\quad x\\in \\Omega, t>0,\\\\ u_t+\\nabla P=\\Delta u+n\\nabla \\phi,\\quad x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0, \\quad x\\in \\Omega, t>0 \\end{array}\\right.$$ under homogeneous boundary conditions of Neumann type for $n$ and $c$, and of Dirichlet type for $u$ in a three-dimensional bounded domains $\\Omega\\subseteq \\mathbb{R}^3$ with smooth boundary, where $\\phi\\in W^{1,\\infty}(\\Omega),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01156","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"}