{"paper":{"title":"Stochastic 3D Leray-$\\alpha$ Model with Fractional Dissipation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Shihu Li, Wei Liu, Yingchao Xie","submitted_at":"2018-05-30T13:26:21Z","abstract_excerpt":"In this paper, we establish the global well-posedness of stochastic 3D Leray-$\\alpha$ model with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equation regularized through a smoothing kernel of order $\\theta_1$ in the nonlinear term and a $\\theta_2$-fractional Laplacian. In the case of $\\theta_1 \\ge 0, \\theta_2 > 0$ and $\\theta_1+\\theta_2 \\geq\\frac{5}{4}$, we prove the global existence and uniqueness of strong solutions. The main results cover many existing works in the deterministic cases, and also generalize some known results of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11939","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"}