{"paper":{"title":"Well-posedness of the supercritical Lane-Emden heat flow in Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Struwe, Simon Blatt","submitted_at":"2015-11-24T12:51:37Z","abstract_excerpt":"For any smoothly bounded domain $\\Omega\\subset\\mathbb R^n$, $n\\geq 3$, and any exponent $p>2^*=2n/(n-2)$ we study the Lane-Emden heat flow $u_t-\\Delta u = |u|^{p-2}u$ on $\\Omega\\times]0,\\infty[$ and establish local and global well-posedness results for the initial value problem with suitably small initial data $u\\big|_{t=0}=u_0$ in the Morrey space $L^{2,\\lambda}(\\Omega)$, where $\\lambda=4/(p-2)$. We contrast our results with results on instantaneous complete blow-up of the flow for certain large data in this space, similar to ill-posedness results of Galaktionov-Vazquez for the Lane-Emden flo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07685","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"}