{"paper":{"title":"Regularity in time of H\\\"older solutions of Euler and hypodissipative Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luigi De Rosa, Maria Colombo","submitted_at":"2018-11-30T16:19:43Z","abstract_excerpt":"In this work we investigate some regularization properties of the incompressible Euler equations and of the fractional Navier-Stokes equations where the dissipative term is given by $(-\\Delta)^\\alpha$, for a suitable power $\\alpha \\in (0,\\frac{1}{2})$ (the only meaningful range for this result). Assuming that the solution $u \\in L^\\infty _t(C^\\theta_x)$ for some $\\theta \\in (0,1)$ we prove that $u \\in C^\\theta_{t,x}$, the pressure $p\\in C^{2\\theta-}_{t,x}$ and the kinetic energy $e \\in C^{\\frac{2\\theta}{1-\\theta}}_t$. This result was obtained for the Euler equations in [Is13] with completely d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12870","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"}