{"paper":{"title":"Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP","math.AP"],"primary_cat":"astro-ph.SR","authors_text":"Hannes Uecker, Ralf Kaiser","submitted_at":"2012-12-13T14:18:25Z","abstract_excerpt":"Given a bounded domain $G \\subset \\R^d$, $d\\geq 3$, we study smooth solutions of a linear parabolic equation with non-constant coefficients in $G$, which at the boundary have to $C^1$-match with some harmonic function in $\\R^d \\setminus \\ov{G}$ vanishing at spatial infinity.\n This problem arises in the framework of magnetohydrodynamics if certain dynamo-generated magnetic fields are considered: For example, in the case of axisymmetry or for non-radial flow fields, the poloidal scalar of the magnetic field solves the above problem. We first investigate the Poisson problem in $G$ with the above "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3180","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"}