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Compared with the argument in \\cite{MiaoWZ:NLS:3d Combined}, the new ingredient is that we use the double duhamel formula in \\cite{Kiv:Clay Lecture, TaoVZ:NLS:mass comp"},"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":"1112.4618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T09:31:54Z","cross_cats_sorted":[],"title_canon_sha256":"d4cda5b5c14913bed3a7e493a16e469e83dd528736124661b745132184f34570","abstract_canon_sha256":"0c6bc72271320fe60bd1f21b1cb75446880b0a87d43cae343d07c96aab6ad7bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:31.807976Z","signature_b64":"PAXETkjaEZkanytis7SysLtiLag7m7R8BwqtWLqj1rLfaCpCHEhPQwqs5wiw17C/l89vSBTe2ZJkSCsxF1zSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d9656dc9f4e459411c108132d537c8247d3c6ee3a350cc8b2991072c80813e0","last_reissued_at":"2026-05-18T01:20:31.807589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:31.807589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dynamics of the NLS with the combined terms in five and higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Guixiang Xu, Lifeng Zhao","submitted_at":"2011-12-20T09:31:54Z","abstract_excerpt":"In this paper, we continue the study in \\cite{MiaoWZ:NLS:3d Combined} to show the scattering and blow-up result of the solution for the nonlinear Schr\\\"{o}dinger equation with the energy below the threshold $m$ in the energy space $H^1(\\R^d)$, iu_t + \\Delta u = -|u|^{4/(d-2)}u + |u|^{4/(d-1)}u, \\; d\\geq 5. \\tag{CNLS} The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \\Delta u = -|u|^{4/(d-2)}u$. 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