{"paper":{"title":"Remarks on global regularity of 2D generalized MHD equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoquan Yuan, Linna Bai","submitted_at":"2013-06-10T13:08:19Z","abstract_excerpt":"In this paper, we investigate the global regularity of 2D generalized MHD equations, in which the dissipation term and magnetic diffusion term are $\\nu(-\\Delta)^\\alpha u$ and $\\eta (-\\Delta)^\\beta b$ respectively. Let $(u_{0}, b_{0})\\in H^{s}$ with $s\\geq2$, it is showed that the smooth solution $(u(x,t),b(x,t))$ is globally regular for the case $ 0\\leq\\alpha\\leq\\{1}{2}, \\alpha+\\beta > \\{3}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2190","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"}