{"paper":{"title":"Optimal decay for the compressible MHD equations in the critical regularity framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiru Wang, Qunyi Bie, Zheng-an Yao","submitted_at":"2019-06-20T12:04:26Z","abstract_excerpt":"In this paper, we study the large time behavior of solutions to the compressible magnetohydrodynamic equations in the $L^p$-type critical Besov spaces. Precisely, we show that if the initial data in the low frequencies additionally belong to some Besov space $\\dot{B}_{2,\\infty}^{-\\sigma_1}$ with $\\sigma_1\\in (1-N/2, 2N/p-N/2]$, then the $\\dot{B}_{p,1}^0$ norm of the critical global solutions presents the optimal decay $t^{-\\frac{N}{2}(\\frac{1}{2}-\\frac{1}{p})-\\frac{\\sigma_1}{2}}$ for $t\\rightarrow+\\infty$. The pure energy argument without the spectral analysis is performed, which allows us to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09119","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"}