{"paper":{"title":"Global existence to a $3D$ chemotaxis-Navier-stokes system with nonlinear diffusion and rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongfang Zhang, Jiashan Zheng, Weifang Yan, Xinhua Zou, Yanyan Li","submitted_at":"2017-06-07T01:58:31Z","abstract_excerpt":"This paper is concerned with the following quasilinear chemotaxis--Navier--Stokes system with nonlinear diffusion and rotation $$ \\left\\{ \\begin{array}{l} n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(nS(x,n,c)\\cdot\\nabla c),\\quad x\\in \\Omega, t>0, c_t+u\\cdot\\nabla c=\\Delta c-nc,\\quad x\\in \\Omega, t>0,\\\\ u_t+\\kappa(u \\cdot \\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi ,\\quad x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0,\\quad x\\in \\Omega, t>0 \\end{array}\\right.\\eqno(CNF) $$ is considered under the no-flux boundary conditions for $n, c$ and the Dirichlet boundary condition for $u$ in a three-dimensional convex dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02022","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"}