{"paper":{"title":"Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit, Xinru Cao","submitted_at":"2016-01-15T12:55:15Z","abstract_excerpt":"The coupled chemotaxis fluid system \\begin{equation} \\left\\{ \\begin{array}{llc} n_t=\\Delta n-\\nabla\\cdot(n S(x,n,c)\\cdot\\nabla c)-u\\cdot\\nabla n, &(x,t)\\in \\Omega\\times (0,T), \\displaystyle c_t=\\Delta c-nc-u\\cdot\\nabla c, &(x,t)\\in\\Omega\\times (0,T), \\displaystyle u_t=\\Delta u-(u\\cdot\\nabla )u+\\nabla P+n\\nabla\\Phi,\\quad \\nabla\\cdot u=0, &(x,t)\\in\\Omega\\times (0,T), \\displaystyle \\nabla c\\cdot\\nu=(\\nabla n-nS(x,n,c)\\cdot\\nabla c)\\cdot\\nu=0, \\;\\; u=0,&(x,t)\\in \\partial\\Omega\\times (0,T), n(x,0)=n_{0}(x),\\quad c(x,0)=c_{0}(x),\\quad u(x,0)=u_0(x) & x\\in\\Omega, \\end{array} \\right. \\end{equation} wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03897","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"}