{"paper":{"title":"Existence theory for stochastic power law fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominic Breit","submitted_at":"2013-12-09T11:09:58Z","abstract_excerpt":"We consider the equations of motion for an incompressible Non-Newtonian fluid in a bounded Lipschitz domain $G\\subset\\mathbb R^d$ during the time intervall $(0,T)$ together with a stochastic perturbation driven by a Brownian motion $W$. The balance of momentum reads as $$dv=\\mathrm{div}\\, S\\,dt-(\\nabla v)v\\,dt+\\nabla\\pi \\,dt+f\\,dt+\\Phi(v)\\,dW_t,$$ where $v$ is the velocity, $\\pi$ the pressure and $f$ an external volume force. We assume the common power law model $S(\\varepsilon(v))=\\big(1+|\\varepsilon(v)|\\big)^{p-2} \\varepsilon(v)$ and show the existence of weak (martingale) solutions provided "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2380","kind":"arxiv","version":4},"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"}