{"paper":{"title":"Local and Global Well-posedness of the fractional order EPDiff equation on $\\mathbb{R}^{d}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boris Kolev, Joachim Escher, Martin Bauer","submitted_at":"2014-11-14T23:38:04Z","abstract_excerpt":"Of concern is the study of fractional order Sobolev--type metrics on the group of $H^{\\infty}$-diffeomorphism of $\\mathbb{R}^{d}$ and on its Sobolev completions $\\mathcal{D}^{q}(\\mathbb{R}^{d})$. It is shown that the $H^{s}$-Sobolev metric induces a strong and smooth Riemannian metric on the Banach manifolds $\\mathcal{D}^{s}(\\mathbb{R}^{d})$ for $s >1 + \\frac{d}{2}$. As a consequence a global well-posedness result of the corresponding geodesic equations, both on the Banach manifold $\\mathcal{D}^{s}(\\mathbb{R}^{d})$ and on the smooth regular Fr\\'echet-Lie group of all $H^{\\infty}$-diffeomorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4081","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"}