{"paper":{"title":"Wellposedness of solution for an $N$-D chemotaxis-convection model during tumor angiogenesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengxiang Zhao, Jiashan Zheng, Kaiqiang Li","submitted_at":"2024-05-27T14:08:48Z","abstract_excerpt":"In this paper, we consider the following parabolic-parabolic-elliptic system } \\begin{align*} \\left\\{\\aligned & u_t=\\Delta u-\\nabla\\cdot(u\\nabla v)+\\xi\\nabla\\cdot(u\\nabla w)+au-\\mu u^{\\alpha}, && x\\in\\Omega, t>0,\\\\ & v_t=\\Delta v+\\nabla\\cdot(v\\nabla w)-v+u,&& x\\in\\Omega, t>0,\\\\ & 0=\\Delta w-w+u,&& x\\in\\Omega, t>0\\\\ \\endaligned\\right. \\end{align*} on a bounded domain $\\Omega\\subset \\mathbb{R}^{N}$ ($N\\geq1$) with smooth boundary $\\partial \\Omega$, where $\\mu$, $a$, $\\alpha$ are positive constants and $\\xi\\in\\mathbb{R}$. If one of the following cases holds:\\\\ (i) $N\\geq4$ and $\\alpha>\\frac{4N-4+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17186","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/2405.17186/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"}