{"paper":{"title":"Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai, Changyou Wang, Junyu Lin","submitted_at":"2013-09-28T04:58:09Z","abstract_excerpt":"We establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in $\\mathbb R^n$ for any initial data ${\\bf m}_0\\in H^1_*(\\mathbb R^n,\\mathbb S^2)$ whose gradient belongs to the Morrey space $M^{2,2}(\\mathbb R^n)$ with small norm $\\displaystyle\\|\\nabla {\\bf m}_0\\|_{M^{2,2}(\\mathbb R^n)}$. The method is based on priori estimates of a dissipative Schr\\\"odinger equation of Ginzburg-Landau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7426","kind":"arxiv","version":1},"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"}