{"paper":{"title":"Blow-up criterion for the $3$D non-resistive compressible Magnetohydrodynamic equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shengguo Zhu, Shuai Xi","submitted_at":"2014-07-29T19:21:14Z","abstract_excerpt":"In this paper, we prove a blow-up criterion in terms of the magnetic field $H$ and the mass density $\\rho$ for the strong solutions to the $3$D compressible isentropic MHD equations with zero magnetic diffusion and initial vacuum. More precisely, we show that the $L^\\infty$ norms of $(H,\\rho)$ control the possible blow-up (see \\cite{olga}\\cite{zx}) for strong solutions, which means that if a solution of the compressible isentropic non-resistive MHD equations is initially smooth and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7831","kind":"arxiv","version":4},"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"}