{"paper":{"title":"Asymptotic behaviors of Landau-Lifshitz flows from $\\Bbb R^2$ to K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lifeng Zhao, Ze Li","submitted_at":"2016-05-04T12:23:46Z","abstract_excerpt":"In this paper, we study the asymptotic behaviors of finite energy solutions to the Landau-Lifshitz flows from $\\Bbb R^2$ into K\\\"ahler manifolds. First, we prove that the solution with initial data below the critical energy converges to a constant map in the energy space as $t\\to \\infty$ for the compact Riemannian surface targets. In particular, when the target is a two dimensional sphere, we prove that the solution to the Landau-Lifshitz-Gilbert equation with initial data having an energy below $4\\pi$ converges to some constant map in the energy space. Second, for general compact K\\\"ahler man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01245","kind":"arxiv","version":2},"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"}