{"paper":{"title":"Global well-posedness and zero-diffusion limit of classical solutions to the 3D conservation laws arising in chemotaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changjiang Zhu, Hongyun Peng, Huanyao Wen","submitted_at":"2012-10-18T11:43:06Z","abstract_excerpt":"In this paper, we study the relationship between a diffusive model and a non-diffusive model which are both derived from the well-known Keller-Segel model, as a coefficient of diffusion $\\varepsilon$ goes to zero. First, we establish the global well-posedness of classical solutions to the Cauchy problem for the diffusive model with smooth initial data which is of small $L^2$ norm, together with some {\\it a priori} estimates uniform for $t$ and $\\varepsilon$. Then we investigate the zero-diffusion limit, and get the global well-posedness of classical solutions to the Cauchy problem for the non-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5101","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"}