{"paper":{"title":"Global weak solutions to a 3-dimensional degenerate and singular chemotaxis-Navier--Stokes system with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Shunsuke Kurima","submitted_at":"2018-02-24T06:12:15Z","abstract_excerpt":"This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term\n  $n_t + u\\cdot\\nabla n =\\Delta n^m - \\chi\\nabla\\cdot(n\\nabla c) + \\kappa n -\\mu n^2$, $x \\in \\Omega,\\ t>0$,\n  $c_t + u\\cdot\\nabla c = \\Delta c - nc$, $x \\in \\Omega,\\ t>0$,\n  $u_t + (u\\cdot\\nabla)u = \\Delta u + \\nabla P + n\\nabla\\Phi, \\quad \\nabla\\cdot u = 0$, $x \\in \\Omega,\\ t>0$, where $\\Omega\\subset \\mathbb{R}^3$ is a bounded domain and $\\chi,\\kappa \\ge 0$ and $m, \\mu >0$. In the above system without fluid environment Jin (J. Differential Equations, 2017) showed existence and boundedness of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08807","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"}