{"paper":{"title":"Global existence and blowup for a class of the focusing 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":"Van Duong Dinh","submitted_at":"2017-11-13T19:02:12Z","abstract_excerpt":"We consider a class of the focusing nonlinear Schr\\\"odinger equation with inverse-square potential \\[ i\\partial_t u + \\Delta u -c|x|^{-2}u = - |u|^\\alpha u, \\quad u(0)=u_0 \\in H^1, \\quad (t,x)\\in \\mathbb{R} \\times \\mathbb{R}^d, \\] where $d\\geq 3$, $\\frac{4}{d}\\leq \\alpha \\leq \\frac{4}{d-2}$ and $c\\ne 0$ satisfies $c>-\\lambda(d):=-\\left(\\frac{d-2}{2}\\right)^2$. In the mass-critical case $\\alpha=\\frac{4}{d}$, we prove the global existence and blowup below ground states for the equation with $d\\geq 3$ and $c>-\\lambda(d)$. In the mass and energy intercritical case $\\frac{4}{d}<\\alpha<\\frac{4}{d-2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04792","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"}