{"paper":{"title":"How strongly does diffusion or logistic-type degradation affect existence of global weak solutions in a chemotaxis-Navier--Stokes system?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami","submitted_at":"2018-10-02T07:27:52Z","abstract_excerpt":"This paper considers the chemotaxis-Navier--Stokes system with nonlinear diffusion and logistic-type degradation term \\begin{align*} \\begin{cases} n_t + u\\cdot\\nabla n = \\nabla \\cdot(D(n)\\nabla n) - \\nabla\\cdot(n \\chi(c) \\nabla c) + \\kappa n - \\mu n^\\alpha, & x\\in \\Omega,\\ t>0, \\\\ c_t + u\\cdot\\nabla c = \\Delta c - nf(c), & x \\in \\Omega,\\ t>0, \\\\ u_t + (u\\cdot\\nabla)u = \\Delta u + \\nabla P + n\\nabla\\Phi + g, \\ \\nabla\\cdot u = 0, & x \\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega\\subset \\mathbb{R}^3$ is a bounded smooth domain; $D \\ge 0$ is a given smooth function such that $D_1 s^{m-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01098","kind":"arxiv","version":2},"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"}