{"paper":{"title":"The fast signal diffusion limit in Keller-Segel(-fluid) systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Yulan Wang, Zhaoyin Xiang","submitted_at":"2018-05-14T16:21:40Z","abstract_excerpt":"This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \\begin{eqnarray*}\n  \\left\\{ \\begin{array}{lcl}\n  \\, \\, \\partial_t n_{\\epsilon} + u_{\\epsilon} \\cdot \\nabla n_{\\epsilon}\n  &=& \\Delta n_{\\epsilon} - \\nabla \\cdot \\Big( n_{\\epsilon} S(x, n_{\\epsilon}, c_{\\epsilon})\\cdot\\nabla c_{\\epsilon}\\Big) + f(x, n_{\\epsilon}, c_{\\epsilon}), \\\\[1mm]\n  \\epsilon \\partial_t c_{\\epsilon} + u_{\\epsilon}\\cdot\\nabla c_{\\epsilon}\n  &=& \\Delta c_{\\epsilon} - c_{\\epsilon} + n_{\\epsilon} , \\\\[1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05263","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"}