{"paper":{"title":"A new approach toward locally bounded global solutions to a $3D$ chemotaxis-stokes system with nonlinear diffusion and rotation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2017-01-05T14:49:44Z","abstract_excerpt":"We consider a degenerate quasilinear chemotaxis--Stokes type involving rotation in the aggregative term, \\begin{equation} \\left\\{\n  \\begin{array}{l}\n  n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(nS(x,n,c)\\cdot\\nabla c),\\quad x\\in \\Omega, t>0,\n  c_t+u\\cdot\\nabla c=\\Delta c-nc, x\\in \\Omega, t>0,\\\\ u_t+\\nabla P=\\Delta u+n\\nabla \\phi ,x\\in \\Omega, t>0,\\\\ \\nabla\\cdot u=0, x\\in \\Omega, t>0,\n  \\end{array}\\right. \\end{equation}\n  where $\\Omega\\subseteq \\mathbb{R}^3$ is a bounded convex domain with smooth boundary.\n  Here $ S\\in C^2(\\bar{\\Omega}\\times[0,\\infty)^2;\\mathbb{R}^{3\\times3})$ is a matrix with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01334","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"}