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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.2380","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-09T11:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"4470bebe354599e8dc0380229467b36b4f65121605eea52b29bfddfa511ad8f8","abstract_canon_sha256":"52adc2e42896741346ea7bed01dfad4233fa35812eea8ba62dd1c0be2dd0ff7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:11.100654Z","signature_b64":"2E1yJkja/ziNqg0yr5UXe1R+luqEmTE1blXOflFa524Z4q27exdxfqlyLX7xfPuvg0QtO5cvuAq3JH8ogF1PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d653c59f690c07fbaf0a0e5360216cd2ed3d2ee9054d94274454c9c30875bbea","last_reissued_at":"2026-05-18T00:53:11.100121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:11.100121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $W$. 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