{"paper":{"title":"Blow-up prevention by nonlinear diffusion in a 2D Keller-Segel-Navier-Stokes system with rotational flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng, Yuanyuan Ke","submitted_at":"2019-03-15T10:25:13Z","abstract_excerpt":"This paper investigates the following Keller-Segel-Navier-Stokes system with nonlinear diffusion and rotational flux $$\\begin{align}\\begin{cases} &n_t+u\\cdot\\nabla n=\\Delta n^m-\\nabla\\cdot(nS(x, n, c)\\nabla c),\\quad &x\\in \\Omega, t>0, \\\\ &c_t+u\\cdot\\nabla c=\\Delta c-c+n,\\quad &x\\in \\Omega, t>0, \\\\ &u_t+\\kappa (u\\cdot\\nabla)u+\\nabla P=\\Delta u+n\\nabla \\phi,\\quad &x\\in \\Omega, t>0, \\\\ &\\nabla\\cdot u=0,\\quad &x\\in \\Omega, t>0, \\end{cases}\\end{align}$$ where $\\kappa\\in \\mathbb{R},\\phi\\in W^{2,\\infty}(\\Omega)$ and $S$ is a given function with values in $\\mathbb{R}^{2\\times2}$ which fulfills $$ |S(x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07536","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"}