{"paper":{"title":"Global existence and blow-up for the Hardy-Sobolev parabolic equation in RN","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Fang, Zhong Tan","submitted_at":"2026-05-24T01:23:39Z","abstract_excerpt":"In this paper, we apply a self-similar transformation to convert the parabolic equation with a Hardy term \\begin{equation*}\n  \\begin{cases}u_t-\\Delta u-\\mu \\frac{u}{|x|^2}=|u|^{2^*-2} u & \\text { in } \\mathbb{R}^N \\times(0, T),\n  u(x, 0)=u_0(x) & \\text { in } \\mathbb{R}^N ,\n  \\end{cases} \\end{equation*} into the following parabolic equation \\begin{equation*}\n  \\begin{cases} v_s-\\Delta v-\\frac{1}{2} y \\cdot \\nabla v=\\beta v+\\frac{\\mu v}{|y|^2}+|v|^{2^*-2} v &\\text { in } \\mathbb{R}^N \\times(0, S),\n  \\left.v\\right|_{s=0}=v_0 & \\text { in } \\mathbb{R}^N, \\end{cases} \\end{equation*} where $N \\geqs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24802","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/2605.24802/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"}