{"paper":{"title":"Unique weak solutions of the non-resistive magnetohydrodynamic equations with fractional dissipation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan Yu, Jiahong Wu, Quansen Jiu, Xiaoxiao Suo","submitted_at":"2019-04-12T02:11:48Z","abstract_excerpt":"This paper examines the uniqueness of weak solutions to the d-dimensional magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\\Delta)^\\alpha u$ and without the magnetic diffusion. Important progress has been made on the standard Laplacian dissipation case $\\alpha=1$. This paper discovers that there are new phenomena with the case $\\alpha<1$. The approach for $\\alpha=1$ can not be directly extended to $\\alpha<1$. We establish that, for $\\alpha<1$, any initial data $(u_0, b_0)$ in the inhomogeneous Besov space $B^\\sigma_{2,\\infty}(\\mathbb R^d)$ with $\\sigma> 1+\\frac{d}{2}-\\alp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06006","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"}