{"paper":{"title":"A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2015-01-21T14:17:00Z","abstract_excerpt":"We consider the parabolic chemotaxis model \\[ u_t=\\Delta u - \\chi \\nabla\\cdot(\\frac uv \\nabla v), \\qquad\\qquad v_t=\\Delta v - v + u\\] in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for $\\chi\\in(0,\\chi_0)$ for some $\\chi_0>1$, thereby proving that the value $\\chi=1$ is not critical in this regard. Our main tool is consideration of the energy functional \\[ \\mathcal{F}_{a,b}(u,v)=\\int_\\Omega u\\ln u - a \\int_\\Omega u\\ln v + b \\int_\\Omega |\\nabla \\sqrt{v}|^2 \\] for $a>0$, $b\\geq 0$, where using nonzero values of $b$ appears to be new in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05175","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"}