{"paper":{"title":"Very mild diffusion enhancement and singular sensitivity: Existence of bounded weak solutions in a two-dimensional chemotaxis-Navier--Stokes system","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2024-11-27T13:35:02Z","abstract_excerpt":"We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \\begin{align*} \\left\\{ \\begin{array}{c@{\\quad}l@{\\quad}l@{\\,}c} n_{t}+u\\cdot\\nabla n=\\nabla\\cdot\\big(D(n)\\nabla n-nS(x,n,c)\\cdot\\nabla c\\big),\\ &x\\in\\Omega,& t>0,\\\\ c_{t}+u\\cdot\\nabla c=\\Delta c-cn,\\ &x\\in\\Omega,& t>0,\\\\ u_{t}+(u\\cdot\\nabla)u=\\Delta u+\\nabla P+n\\nabla\\Phi,\\quad \\nabla\\cdot u=0,\\ &x\\in\\Omega,& t>0,\\\\ \\big(D(n)\\nabla n-nS(x,n,c)\\cdot\\nabla c)\\cdot\\nu=\\nabla c\\cdot\\nu=0,\\ u=0,\\ &x\\in\\partial\\Omega,& t>0,\\\\ n(\\cdot,0)=n_0,\\ c(\\cdot,0)=c_0,\\ u(\\cdot,0)=u_0,\\ &x\\in\\Omega. \\end{array}\\right. \\end{a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18336","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18336/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}