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By means of the localized virial estimate, we prove that the ground state standing wave is strongly unstable by blow-up. This result is a complement to a recent result of Peng-Shi [J. Math. Phys. 59 (2018), 011508] where the stability and instability of standing waves were studied in the $L^2$-subcritical and $L^2$-critic"},"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":"1806.08935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-23T09:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"fd124aecbe95ca7fdc38557dae4d23ae0f822cc2e0559bdb83deb73ae733a7ad","abstract_canon_sha256":"148fea7201076406176447aedd3a33c90b73c9f9b99ab3a3619580e52f0f6509"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:33.756596Z","signature_b64":"cGo0doYY9cCSKauW2efOBRk7XGN1FNRTVFoejHcqzLtq/8KQ/15CNQeppkXl1WVY2aJXLup29cxhpliqqTC9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e67bdc3453948cba81141c50569ee3293bd88fe6acf29e4d3c9e61cfa14a8e2e","last_reissued_at":"2026-05-17T23:51:33.755985Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:33.755985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On instability of standing waves for the mass-supercritical fractional nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2018-06-23T09:42:40Z","abstract_excerpt":"We consider the focusing $L^2$-supercritical fractional nonlinear Schr\\\"odinger equation \\[ i\\partial_t u - (-\\Delta)^s u = -|u|^\\alpha u, \\quad (t,x) \\in \\mathbb{R}^+ \\times \\mathbb{R}^d, \\] where $d\\geq 2, \\frac{d}{2d-1} \\leq s <1$ and $\\frac{4s}{d}<\\alpha<\\frac{4s}{d-2s}$. By means of the localized virial estimate, we prove that the ground state standing wave is strongly unstable by blow-up. This result is a complement to a recent result of Peng-Shi [J. Math. 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