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In particular, these include the energy space $H^1\\times L^2$. Our results improve the previous ones obtained in \\cite{Bidegaray1}, \\cite{Bidegaray2} and \\cite{Corcho-Linares}. Moreover, in the critical case (N=2) and for initial data in $H^1\\times L^2$, we prove that solutions exist for all times, thus providing a negative answer to the open pr"},"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":"1102.2874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-14T20:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"3f37d97c74f92790f461bda66a221936b0b477775640470932f356689957700f","abstract_canon_sha256":"746e9e497ad54e62bc6d34311d9db8501495e1040a88c412b9053fd9eab600a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:54.926846Z","signature_b64":"GMVog+t30RFj6sDCVzVcxz064now87ixUEu6jf9vQRp5+f5yzOHtlj+Ivdow7k8qj5Q0ezseL5MvLNcBbMugCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59abf45cc416b36e635ca3a9819ee85a084ebaacab161aef016a629d7f91fa6a","last_reissued_at":"2026-05-18T03:52:54.926305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:54.926305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local and Global Well-Posedness for the Critical Schrodinger-Debye System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adan J. Corcho, Filipe Oliveira, Jorge Drumond Silva","submitted_at":"2011-02-14T20:08:16Z","abstract_excerpt":"We establish local well-posedness results for the Initial Value Problem associated to the Schr\\\"odinger-Debye system in dimensions $N=2, 3$ for data in $H^s\\times H^{\\ell}$, with $s$ and $\\ell$ satisfying $\\max \\{0, s-1\\} \\le \\ell \\le \\min\\{2s, s+1\\}$. In particular, these include the energy space $H^1\\times L^2$. Our results improve the previous ones obtained in \\cite{Bidegaray1}, \\cite{Bidegaray2} and \\cite{Corcho-Linares}. 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