{"paper":{"title":"Global solutions to Stokes-Magneto equations with fractional dissipations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hantaek Bae, Hyunwoo Kwon, Jaeyong Shin","submitted_at":"2023-10-05T02:16:41Z","abstract_excerpt":"In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $\\mathbb{T}^{d}$ and establish the local and global well-posedness with initial magnetic field $\\mathbf{b}_0\\in H^{s}(\\mathbb{T}^d)$. We also show the existence of a unique mild solution of the resistive case with initial data $\\mathbf{b}_0$ in the critical $L^{p}(\\mathbb{R}^d)$ space. Moreover, we show that $\\|\\mathbf{b}(t)\\|_{L^{p}}$ converges to zero as $t\\rightarrow\\infty$ when the initial data is sufficiently small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.03255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.03255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}