{"paper":{"title":"An optimal result for global existence and boundedness in a three-dimensional Keller-Segel(-Navier)-Stokes system (involving a tensor-valued sensitivity with saturation)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-06-19T07:07:04Z","abstract_excerpt":"The coupled quasilinear Keller-Segel-Navier-Stokes system $$\n  \\left\\{\n  \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n-\\nabla\\cdot(nS(x,n,c)\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-c+n,\\quad x\\in \\Omega, t>0, u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi,\\quad x\\in \\Omega, t>0, \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(KSNF)\n  $$ is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\\Omega\\subseteq \\mathbb{R}^3$ with smooth boundary, where $\\kappa\\in \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07067","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"}