{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AM4W4RU2J5ZVNUGR6ZA5B7S7X6","short_pith_number":"pith:AM4W4RU2","schema_version":"1.0","canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","source":{"kind":"arxiv","id":"1701.01242","version":1},"attestation_state":"computed","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."},"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":"1701.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"da951949477519412c500d08fc0fa81a78fe6f36ee22eb20dae39848c0062062","abstract_canon_sha256":"398d8fcf04c2d96d41a5b38d69aa39e9704724627ce7cac730bae951402ae46b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:20.084030Z","signature_b64":"RjrSKnZ01djdd9aRDR5GiscdJTOxnCC1uX/Mj1ygXthg5bQxjKQkBLw8IsTZwwqEoWvAPFrSu/t2mz7w53u6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","last_reissued_at":"2026-05-18T00:53:20.083571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:20.083571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.01242","created_at":"2026-05-18T00:53:20.083636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.01242v1","created_at":"2026-05-18T00:53:20.083636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01242","created_at":"2026-05-18T00:53:20.083636+00:00"},{"alias_kind":"pith_short_12","alias_value":"AM4W4RU2J5ZV","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AM4W4RU2J5ZVNUGR","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AM4W4RU2","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6","json":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6.json","graph_json":"https://pith.science/api/pith-number/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/graph.json","events_json":"https://pith.science/api/pith-number/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/events.json","paper":"https://pith.science/paper/AM4W4RU2"},"agent_actions":{"view_html":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6","download_json":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6.json","view_paper":"https://pith.science/paper/AM4W4RU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.01242&json=true","fetch_graph":"https://pith.science/api/pith-number/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/graph.json","fetch_events":"https://pith.science/api/pith-number/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/action/storage_attestation","attest_author":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/action/author_attestation","sign_citation":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/action/citation_signature","submit_replication":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/action/replication_record"}},"created_at":"2026-05-18T00:53:20.083636+00:00","updated_at":"2026-05-18T00:53:20.083636+00:00"}