{"paper":{"title":"MHS equilibria in the non-resistive limit to the randomly forced resistive magnetic relaxation equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federico Pasqualotto, In-Jee Jeong, Ken Abe, Naoki Sato","submitted_at":"2025-06-10T03:00:53Z","abstract_excerpt":"We consider randomly forced resistive magnetic relaxation equations (MRE) with resistivity $\\kappa>0$ and a force proportional to $\\sqrt{\\kappa}\\ $ on the flat $d$-torus $\\mathbb{T}^{d}$ for $d\\geq 2$. We show the path-wise global well-posedness of the system and the existence of the invariant measures, and construct a random magnetohydrostatic (MHS) equilibrium $B(x)$ in $H^{1}(\\mathbb{T}^{d})$ with law $D(B)=\\mu$ as a non-resistive limit $\\kappa\\to 0$ of statistically stationary solutions $B_{\\kappa}(x,t)$. For $d=2$, the measure $\\mu$ does not concentrate on any compact sets in $H^{1}(\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08394","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/2506.08394/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"}