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Assuming that the solution blows up in a finite time $t^* < \\infty$, we establish a lower bound for the rate of blow-up of the corresponding Sobolev norms in the form $$ \\|\\psi(t)\\|_{H^{\\ell+1/2}} +\\|n(t)\\|_{H^{\\ell}} + \\|n_t(t)\\|_{H^{\\ell-1}} > C(t^*-t)^{-\\theta_\\ell} $$ with $\\theta_\\ell = \\frac{1}{4}(1+ 2 \\ell)^-$. The analysis is a reappraisal of the local wellposedness theory of Ginibre, Tsutsumi and Velo (1997) combined"},"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":"1305.0324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-02T01:33:48Z","cross_cats_sorted":[],"title_canon_sha256":"8006b9971d5fbef095f0383552647a870e47852c2756a181c076b3037c43c881","abstract_canon_sha256":"b55c1b6e9cecda96b04440820336c4d64ff31034a5134e63e6ec3ce4b42458de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:40.575234Z","signature_b64":"Szl0I9vZy3WZuKLMniywLuK0B0FPiYBbDo8Y8VJ9NJmhJU9pKo+LCClMD5BmysgvNTIsGasE2MI+1MMG6btHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f18ee69dded768793f0faf2b367b22a71f5cf03cb732aeb626a9227f6c7d6a84","last_reissued_at":"2026-05-18T03:26:40.574683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:40.574683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bound for the rate of blow-up of singular solutions of the Zakharov system in $\\R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Sulem, J. Colliander, M. Czubak","submitted_at":"2013-05-02T01:33:48Z","abstract_excerpt":"We consider the scalar Zakharov system in $\\R^3$ for initial conditions $(\\psi(0), n(0), n_t(0)) \\in H^{\\ell+1/2} \\times H^\\ell \\times H^{\\ell-1} $,\n  $0\\leq\\ell \\leq 1$. Assuming that the solution blows up in a finite time $t^* < \\infty$, we establish a lower bound for the rate of blow-up of the corresponding Sobolev norms in the form $$ \\|\\psi(t)\\|_{H^{\\ell+1/2}} +\\|n(t)\\|_{H^{\\ell}} + \\|n_t(t)\\|_{H^{\\ell-1}} > C(t^*-t)^{-\\theta_\\ell} $$ with $\\theta_\\ell = \\frac{1}{4}(1+ 2 \\ell)^-$. 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