{"paper":{"title":"A strengthening of the energy inequality for the Leray-Hopf solutions of the 3D periodic Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Radu Dascaliuc","submitted_at":"2010-10-26T22:50:41Z","abstract_excerpt":"In present note we establish the following inequality for the the Leray-Hopf solutions of the 3-D $\\Omega$-periodic Navier-Stokes Equations: \\[\\phi(|u(t)|^2)-\\phi(|u(t_0)|^2)\\le 2\\int_{t_0}^{t}\\phi'(|u(\\tau)|^2) [-\\nu|A^{1/2}u(\\tau)|^2+(g(\\tau),u(\\tau))]\\,d\\tau\\] for all $t_0$ Leray-Hopf points, $t\\ge t_0$, and $\\phi:\\mathbb{R}_{+}\\to\\mathbb{R}$ is an absolutely continouos non-decreasing function with bounded derivative. %with $\\phi'(\\xi)\\ge0$ for all $\\xi>0$. Here $(\\cdot,\\cdot)$ and $|\\cdot|$ is correspondingly the $L^2$ inner product and the $L^2$ norm on $\\Omega$, and $A$ is the Stokes ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5535","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"}