{"paper":{"title":"Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller--Segel-Stokes system with competitive kinetics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Shunsuke Kurima, Xinru Cao","submitted_at":"2017-06-24T05:51:52Z","abstract_excerpt":"This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\\cdot\\nabla n_1 =\\Delta n_1 - \\chi_1\\nabla\\cdot(n_1\\nabla c)+ \\mu_1n_1(1- n_1 - a_1n_2)$, $(n_2)_t + u\\cdot\\nabla n_2 =\\Delta n_2 - \\chi_2\\nabla\\cdot(n_2\\nabla c) + \\mu_2n_2(1- a_2n_1 - n_2), c_t + u\\cdot\\nabla c =\\Delta c - c + \\alpha n_1 +\\beta n_2$, $u_t= \\Delta u + \\nabla P+ (\\gamma n_1 + \\delta n_2)\\nabla\\phi$, $ \\nabla\\cdot u = 0$ under homogeneous Neumann boundary conditions in a bounded domain $\\Omega \\subset \\mathbb{R}^3$ with smooth boundary. Many mathematicians study chemotaxis-fl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07910","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"}