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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.09153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-22T09:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"6b93e27f6c11b048230997986b44d9abe6ea70d1c7a8b88b579636d0e3833600","abstract_canon_sha256":"577a40a30a913867b54c230f6d2d8a8609c5d80913753f3e5bee066b6010a51b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:24.524278Z","signature_b64":"7sgj6qb2r2uIvIds3jzqD/dUBoKPWpBchBZzdnU0stmFzm1m61rFV1US1S5444dOJaKPlLGcazErnhL1b2QtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79aee32a0cab27c84e3cdcf794395e95c2dd5abe168d423f218b1072c407a1be","last_reissued_at":"2026-05-18T00:02:24.523620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:24.523620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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