{"paper":{"title":"Note on the Euler equations in C^k spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Tarek M. Elgindi","submitted_at":"2014-05-13T16:24:58Z","abstract_excerpt":"In this note, using the ideas from our recent article \\cite{EM}, we prove strong ill-posedness for the 2D Euler equations in $C^k$ spaces. This note provides a significantly shorter proof of many of the main results in \\cite{BLi2}. In the case $k>1$ we show the existence of initial data for which the $kth$ derivative of the velocity field develops a logarithmic singularity immediately. The strong ill-posedness covers $C^{k-1,1}$ spaces as well. The ill-posedness comes from the pressure term in the Euler equation. We formulate the equation for $D^k u$ as:\n  $$\\partial_t D^k u=D^{k+1} p + l.o.t."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7891","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"}