{"paper":{"title":"Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2014-07-18T19:25:12Z","abstract_excerpt":"We prove existence of global weak solutions to the chemotaxis system\n  $ u_t=\\Delta u - \\nabla\\cdot (u\\nabla v) +\\kappa u -\\mu u^2 $\n  $ v_t=\\Delta v-v+u $\n  under homogeneous Neumann boundary conditions in a smooth bounded convex domain $\\Omega\\subset R^n$, for arbitrarily small values of $\\mu>0$.\n  Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that $\\kappa$ is not too large. In this case, we also consider their large-time behaviour: We prove decay if $\\kappa\\leq 0$ and the existence of an absorbing set if $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5085","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"}