{"paper":{"title":"Existence of a martingale weak solution to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with a stochastic perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huaqiao Wang, Yucong Wang, Zhong Tan","submitted_at":"2017-01-05T08:27:43Z","abstract_excerpt":"In this paper, we consider the stochastic %equations of incompressible non-Newtonian fluids driven by a cylindrical Wiener process $W$ with shear rate dependent on viscosity in a bounded Lipschitz domain $D\\in \\mathbb{R}^n$ during the time interval $(0,T)$. For $q>\\frac{2n+2}{n+2}$ in the growth conditions (1.2), we prove the existence of a martingale weak solution with $\\nabla\\cdot u=0$ by using a pressure decomposition which is adapted to the stochastic setting, the stochastic compactness method and the $L^\\infty$-truncation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01242","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"}