{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3XEDS6KV45UJF57FMABK5AKIYG","short_pith_number":"pith:3XEDS6KV","schema_version":"1.0","canonical_sha256":"ddc8397955e76892f7e56002ae8148c1a5b37f5741dbdc4040a625256ba3d261","source":{"kind":"arxiv","id":"1509.05211","version":1},"attestation_state":"computed","paper":{"title":"Isotropic realizability of a strain field for the incompressible two-dimensional Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marc Briane (IRMAR)","submitted_at":"2015-09-17T11:30:14Z","abstract_excerpt":"In the paper we study the problem of the isotropic realizability in R^2 of a regular strain field e(U)=1/2(DU+DU^T) for the incompressible Stokes equation, namely the existence of a positive viscosity mu\\textgreater{}0 solving the Stokes equation in R^2 with the prescribed field e(U). We show that if e(U) does not vanish at some point, then the isotropic realizability holds in the neighborhood of that point. The global realizability in R^2 or in the torus is much more delicate, since it involves the global existence of a regular solution to a semilinear wave equation the coefficients of which "},"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":"1509.05211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-17T11:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"664195e7abb27f94e6d5d595d467294522b06af46abda6237b373e085b6594fa","abstract_canon_sha256":"7041b89a3e12d7809786327dcbb9ab3628b629f4f2fca16b750476fb38b0ac31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:49.598623Z","signature_b64":"QPaisSvC4JAWE2TIa5udjLWkCgdn8O5jw5D3VFbwNeM/Hd2L+DwN15dQ0vS7JuA+eE6VUg62WinEVoi+Yw7+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddc8397955e76892f7e56002ae8148c1a5b37f5741dbdc4040a625256ba3d261","last_reissued_at":"2026-05-18T01:32:49.598056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:49.598056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isotropic realizability of a strain field for the incompressible two-dimensional Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marc Briane (IRMAR)","submitted_at":"2015-09-17T11:30:14Z","abstract_excerpt":"In the paper we study the problem of the isotropic realizability in R^2 of a regular strain field e(U)=1/2(DU+DU^T) for the incompressible Stokes equation, namely the existence of a positive viscosity mu\\textgreater{}0 solving the Stokes equation in R^2 with the prescribed field e(U). We show that if e(U) does not vanish at some point, then the isotropic realizability holds in the neighborhood of that point. The global realizability in R^2 or in the torus is much more delicate, since it involves the global existence of a regular solution to a semilinear wave equation the coefficients of which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05211","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":"1509.05211","created_at":"2026-05-18T01:32:49.598123+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05211v1","created_at":"2026-05-18T01:32:49.598123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05211","created_at":"2026-05-18T01:32:49.598123+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XEDS6KV45UJ","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XEDS6KV45UJF57F","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XEDS6KV","created_at":"2026-05-18T12:29:02.477457+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/3XEDS6KV45UJF57FMABK5AKIYG","json":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG.json","graph_json":"https://pith.science/api/pith-number/3XEDS6KV45UJF57FMABK5AKIYG/graph.json","events_json":"https://pith.science/api/pith-number/3XEDS6KV45UJF57FMABK5AKIYG/events.json","paper":"https://pith.science/paper/3XEDS6KV"},"agent_actions":{"view_html":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG","download_json":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG.json","view_paper":"https://pith.science/paper/3XEDS6KV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05211&json=true","fetch_graph":"https://pith.science/api/pith-number/3XEDS6KV45UJF57FMABK5AKIYG/graph.json","fetch_events":"https://pith.science/api/pith-number/3XEDS6KV45UJF57FMABK5AKIYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG/action/storage_attestation","attest_author":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG/action/author_attestation","sign_citation":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG/action/citation_signature","submit_replication":"https://pith.science/pith/3XEDS6KV45UJF57FMABK5AKIYG/action/replication_record"}},"created_at":"2026-05-18T01:32:49.598123+00:00","updated_at":"2026-05-18T01:32:49.598123+00:00"}