{"paper":{"title":"On the Galerkin approximation and strong norm bounds for the stochastic Navier-Stokes equations with multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Igor Kukavica, Kerem Ugurlu, Mohammed Ziane","submitted_at":"2018-06-05T05:16:24Z","abstract_excerpt":"We investigate the convergence of the Galerkin approximation for the stochastic Navier-Stokes equations in an open bounded domain $\\mathcal{O}$ with the non-slip boundary condition. We prove that\n  \\begin{equation*}\n  \\mathbb{E} \\left[ \\sup_{t \\in [0,T]} \\phi_1(\\lVert (u(t)-u^n(t))\n  \\rVert^2_V) \\right] \\rightarrow 0\n  \\end{equation*} as $n \\rightarrow \\infty$ for any deterministic time $T > 0$ and for a specified moment function $\\phi_1(x)$ where $u^n(t,x)$ denotes the Galerkin approximation of the solution $u(t,x)$. Also, we provide a result on uniform boundedness of the moment $\\mathbb{E} ["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01498","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"}