{"paper":{"title":"On the ideal magnetohydrodynamics in three-dimensional thin domains: well-posedness and asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Xu","submitted_at":"2017-07-09T08:56:21Z","abstract_excerpt":"We consider the ideal magnetohydrodynamics (MHD) subjected to a strong magnetic field along $x_1$ direction in three-dimensional thin domains $\\Omega_\\delta=\\mathbb{R}^2\\times(-\\delta,\\delta)$ with slip boundary conditions. It is well-known that in this situation the system will generate Alfv\\'en waves. Our results are summarized as follows:\n  (i).\\, We construct the global solutions (Alfv\\'en waves) to MHD in the thin domain $\\Omega_\\delta$ with $\\delta>0$. In addition, the uniform energy estimates are obtained with respected to the parameter $\\delta$.\n  (ii). We justify the asymptotics of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02544","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"}