{"paper":{"title":"Turbulent flows as generalized Kelvin-Voigt materials: modeling and analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cherif Amrouche, Dinh Duong Nguyen, Luigi C. Berselli, Roger Lewandowski","submitted_at":"2019-07-22T09:01:51Z","abstract_excerpt":"We model a 3D turbulent fluid, evolving toward a statistical equilibrium, by adding to the equations for the mean field $(v, p)$ a term like $-\\alpha \\nabla\\cdot(\\ell(x) D v_t)$. This is of the Kelvin-Voigt form, where the Prandtl mixing length $\\ell$ is not constant and vanishes at the solid walls. We get estimates for velocity $v$ in $L^\\infty_t H^1_x \\cap W^{1,2}_t H^{1/2}_x$, that allow us to prove the existence and uniqueness of a regular-weak solutions $(v, p)$ to the resulting system, for a given fixed eddy viscosity. We then prove a structural compactness result that highlights the rob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09191","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"}