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We prove a Gagliardo-Nirenberg type estimate and use it to establish sufficient conditions for global existence and blow-up in $H^1(\\mathbb{R}^N)$."},"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":"1610.06901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T19:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"626bfe1352d70e150cc505ede3246f349a0a2ea5550ffaba2beb92c4bc6629c1","abstract_canon_sha256":"bfdd216708216e428a08436fcee5ef079ff5b878fc669c24c689b671d2c4a5c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.476756Z","signature_b64":"/ceF3bmeMOebaYXJ5a/yzqfQHFxtmHDpbqu3X/KfmlCCqGm5zw0ru2+EaYh8w2osLCNODjT+IhbFZsS9vz14AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab929828a3c44ab3cdc3311891141e80bf38c5eea3335918f20f0ecc02e4b369","last_reissued_at":"2026-05-18T01:01:36.476274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.476274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global well-posedness and blow-up on the energy space for the Inhomogeneous Nonlinear Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luiz Gustavo Farah","submitted_at":"2016-10-21T19:26:48Z","abstract_excerpt":"We consider the supercritical inhomogeneous nonlinear Schr\\\"odinger equation (INLS)\n  $$i\\partial_t u+\\Delta u+|x|^{-b}|u|^{2\\sigma}u=0,$$ where $(2-b)/N<\\sigma<(2-b)/(N-2)$ and $0<b<\\min\\{2,N\\}$. 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