{"paper":{"title":"The Euler equations in a critical case of the generalized Campanato space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongho Chae, Joerg Wolf","submitted_at":"2019-04-18T10:38:54Z","abstract_excerpt":"In this paper we prove local in time well-posedness for the incompressible Euler equations in $\\Bbb R^n$ for the initial data in $\\mathscr {L}^{ 1}_{ 1(1)}(\\mathbb {R}^{n}) $, which corresponds to a critical case of the generalized Campanato spaces $ \\mathscr {L}^{ s}_{ q(N)}(\\mathbb {R}^{n})$. The space is studied extensively in our companion paper\\cite{trans}, and in the critical case we have embeddings $ B^{1}_{\\infty, 1} (\\Bbb R^n) \\hookrightarrow \\mathscr {L}^{ 1}_{ 1(1)}(\\mathbb {R}^{n}) \\hookrightarrow C^{0, 1} (\\Bbb R^n)$, where $B^{1}_{\\infty, 1} (\\Bbb R^n)$ and $ C^{0, 1} (\\Bbb R^n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08676","kind":"arxiv","version":2},"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"}