{"paper":{"title":"On Global Regularity of 2D Generalized Magnetohydrodynamic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Chuong V. Tran, Xinwei Yu, Zhichun Zhai","submitted_at":"2013-02-27T00:33:48Z","abstract_excerpt":"In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $- \\nu (- \\triangle)^{\\alpha} u$ and $- \\kappa (-\\triangle)^{\\beta} b$. We show that smooth solutions are global in the following three cases: $\\alpha \\geqslant 1 / 2, \\beta \\geqslant 1$; $0 \\leqslant \\alpha < 1 / 2, 2 \\alpha + \\beta > 2$; $\\alpha \\geqslant 2, \\beta = 0$. We also show that in the inviscid case $\\nu = 0$, if $\\beta > 1$, then smooth solutions are global as long as the direction of the magnetic field remains smooth enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6633","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"}