{"paper":{"title":"Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2019-05-20T01:58:45Z","abstract_excerpt":"We consider an initial-boundary value problem for the incompressible four-component Keller-Segel-Navier-Stokes system with rotational flux $$\\left\\{\\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n-\\nabla\\cdot(nS(x,n,c)\\nabla c)-nm,\\quad x\\in \\Omega, t>0,\\\\ c_t+u\\cdot\\nabla c=\\Delta c-c+m,\\quad x\\in \\Omega, t>0,\\\\ m_t+u\\cdot\\nabla m=\\Delta m-nm,\\quad x\\in \\Omega, t>0,\\\\ u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+(n+m)\\nabla \\phi,\\quad x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.$$ in a bounded domain $\\Omega\\subset \\mathbb{R}^3$ with smooth boundary, where $\\kapp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08647","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"}