{"paper":{"title":"On the Helicity conservation for the incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luigi De Rosa","submitted_at":"2018-12-03T11:35:38Z","abstract_excerpt":"In this work we investigate the helicity regularity for weak solutions of the incompressible Euler equations. To prove regularity and conservation of the helicity we will threat the velocity $u$ and its $curl\\, u$ as two independent functions and we mainly show that the helicity is a constant of motion assuming $u \\in L^{2r}_t(C^\\theta_x)$ and $curl \\,u \\in L^{\\kappa}_t(W^{\\alpha,1}_x)$ where $r,\\kappa $ are conjugate H\\\"older exponents and $2\\theta+\\alpha \\geq 1$. Using the same techniques we also show that the helicity has a suitable H\\\"older regularity even in the range where it is not nece"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00678","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"}