{"paper":{"title":"Continuity of the solution map of the Euler equations in H\\\"older spaces and weak norm inflation in Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gerard Misio{\\l}ek, Tsuyoshi Yoneda","submitted_at":"2016-01-06T00:08:23Z","abstract_excerpt":"We construct an example showing that the solution map of the Euler equations is not continuous in the H\\\"older space from $C^{1,\\alpha}$ to $L^\\infty_tC^{1,\\alpha}_x$ for any $0<\\alpha<1$. On the other hand we show that it is continuous when restricted to the little H\\\"older subspace $c^{1,\\alpha}$. We apply the latter to prove an ill-posedness result for solutions of the vorticity equations in Besov spaces near the critical space $B^1_{2,1}$. As a consequence we show that a sequence of best constants of the Sobolev embedding theorem near the critical function space is not continuous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01024","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"}