{"paper":{"title":"On the Unboundedness of Higher Regularity Sobolev Norms of Solutions for the Critical Schr\\\"odinger-Debye System with Vanishing Relaxation Delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ad\\'an J. Corcho, Jorge Drumond Silva","submitted_at":"2015-10-08T18:37:02Z","abstract_excerpt":"We consider the Schr\\\"odinger-Debye system in $\\mathbb{R}^n$, for $n=3,4$. Developing on previously known local well-posedness results, we start by establishing global well-posedness in $H^1(\\mathbb{R}^3)\\times L^2(\\mathbb{R}^3)$ for a broad class of initial data. We then concentrate on the initial value problem in $n=4$, which is the energy-critical dimension for the corresponding cubic nonlinear Schr\\\"odinger equation. We start by proving local well-posedness in $H^1(\\mathbb{R}^4)\\times H^1(\\mathbb{R}^4)$. Then, for the focusing case of the system, we derive a virial type identity and use it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02434","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"}