{"paper":{"title":"Blow-up of the radially symmetric solutions for the quadratic nonlinear Schr\\\"{o}dinger system without mass-resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kuranosuke Nishimura, Nobu Kishimoto, Takahisa Inui","submitted_at":"2018-10-22T09:43:03Z","abstract_excerpt":"We consider the quadratic nonlinear Schr\\\"{o}dinger system \\begin{align*}\n  \\begin{cases} i\\partial_t u +\\Delta u =v \\overline{u},\\\\ i\\partial_t v +\\kappa \\Delta v =u^2, \\end{cases}\n  \\text{ on } I \\times \\mathbb{R}^d, \\end{align*} where $1\\leq d \\leq 6$ and $\\kappa>0$. In the lower dimensional case $d=1,2,3$, it is known that the $H^1$-solution is global in time. On the other hand, there are finite time blow-up solutions when $d=4,5,6$ and $\\kappa=1/2$. The condition of $\\kappa=1/2$ is called mass-resonance. In this paper, we prove finite time blow-up under radially symmetric assumption when "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09153","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"}