{"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}. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2874","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}