{"paper":{"title":"Onsager's conjecture for admissible weak solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camillo De Lellis, L\\'aszl\\'o Sz\\'ekelyhidi Jr., Tristan Buckmaster, Vlad Vicol","submitted_at":"2017-01-30T16:22:12Z","abstract_excerpt":"We prove that given any $\\beta<1/3$, a time interval $[0,T]$, and given any smooth energy profile $e \\colon [0,T] \\to (0,\\infty)$, there exists a weak solution $v$ of the three-dimensional Euler equations such that $v \\in C^{\\beta}([0,T]\\times \\mathbb{T}^3)$, with $e(t) = \\int_{\\mathbb{T}^3} |v(x,t)|^2 dx$ for all $t\\in [0,T]$. Moreover, we show that a suitable $h$-principle holds in the regularity class $C^\\beta_{t,x}$, for any $\\beta<1/3$. The implication of this is that the dissipative solutions we construct are in a sense typical in the appropriate space of subsolutions as opposed to just "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08678","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"}