{"paper":{"title":"Mass concentration and characterization of finite time blow-up solutions for the nonlinear Schr\\\"odinger equation with inverse-square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelwahab Bensouilah, Van Duong Dinh","submitted_at":"2018-04-23T21:43:49Z","abstract_excerpt":"We consider the $L^2$-critical NLS with inverse-square potential\n  $$\n  i \\partial_t u +\\Delta u + c|x|^{-2} u = -|u|^{\\frac{4}{d}} u, \\quad u(0) = u_0, \\quad (t,x) \\in \\mathbb{R}^+ \\times \\mathbb{R}^d,\n  $$\n  where $d\\geq 3$ and $c\\ne 0$ satisfies $c<\\lambda(d) := \\left(\\frac{d-2}{2}\\right)^2$. Using a refined compactness lemma, we extend the mass concentration of finite time blow-up solutions established in the attractive case by the first author in [Bensouilah] to $c<\\lambda(d)$. By means of a simple and short limiting profile theorem, we get the same classification result obtained by Csobo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08752","kind":"arxiv","version":2},"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"}