{"paper":{"title":"Global solvability of chemotaxis-fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2018-07-06T13:34:03Z","abstract_excerpt":"In this work we extend a recent result to chemotaxis fluid systems which include matrix-valued sensitivity functions $S(x,n,c):\\Omega\\times[0,\\infty)^2\\to\\mathbb{R}^{3\\times3}$ in addition to the porous medium type diffusion, which were discussed in the previous work. Namely, we will consider the system \\begin{align*} \\left\\{ \\begin{array}{r@{\\,}c@{\\,}c@{\\ }l@{\\quad}l@{\\quad}l@{\\,}c} n_{t}&+&u\\cdot\\!\\nabla n&=\\Delta n^m-\\nabla\\!\\cdot(nS(x,n,c)\\nabla c),\\ &x\\in\\Omega,& t>0,\\\\ c_{t}&+&u\\cdot\\!\\nabla c&=\\Delta c-c+n,\\ &x\\in\\Omega,& t>0,\\\\ u_{t}&+&(u\\cdot\\nabla)u&=\\Delta u+\\nabla P+n\\nabla\\phi,\\ &"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02404","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"}