{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:E6WMCUOZYGYAYAO6KJIUSFWKKA","short_pith_number":"pith:E6WMCUOZ","canonical_record":{"source":{"id":"1905.12900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-30T07:50:07Z","cross_cats_sorted":[],"title_canon_sha256":"6a5a328585a17567aa0cf5f8b2fb81c3096f6c16f4857db98bafe3b6d2d8b352","abstract_canon_sha256":"89792cf4dc09a0feda929ab1b97395fb16fa2c3381f8e044049283be04cda361"},"schema_version":"1.0"},"canonical_sha256":"27acc151d9c1b00c01de52514916ca5039aa532c7ad815aed84d31fe1b32041d","source":{"kind":"arxiv","id":"1905.12900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12900","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12900v1","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12900","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"E6WMCUOZYGYA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E6WMCUOZYGYAYAO6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E6WMCUOZ","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:E6WMCUOZYGYAYAO6KJIUSFWKKA","target":"record","payload":{"canonical_record":{"source":{"id":"1905.12900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-30T07:50:07Z","cross_cats_sorted":[],"title_canon_sha256":"6a5a328585a17567aa0cf5f8b2fb81c3096f6c16f4857db98bafe3b6d2d8b352","abstract_canon_sha256":"89792cf4dc09a0feda929ab1b97395fb16fa2c3381f8e044049283be04cda361"},"schema_version":"1.0"},"canonical_sha256":"27acc151d9c1b00c01de52514916ca5039aa532c7ad815aed84d31fe1b32041d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:39.380987Z","signature_b64":"JTp4/I4jXkTn8faA0hgDY1SxxxkugxKwDbve19+/XF9/el5qIkbl1A7tpzH21Z4YhFFshzTZoxvnC5fzDRNGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27acc151d9c1b00c01de52514916ca5039aa532c7ad815aed84d31fe1b32041d","last_reissued_at":"2026-05-17T23:44:39.380424Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:39.380424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.12900","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQR7rFKdn6CztNSMEsHdVv7TFyni8oWhBwyhzcIo1CR2A3iweXga/r0qI0rHtOVoxpE5Qf/LJ1Itqvl9TaUMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:24:04.558534Z"},"content_sha256":"22a949ff8179e74d6610afd1a3a3a97e56f808b664c98976d1a55441c8e643f8","schema_version":"1.0","event_id":"sha256:22a949ff8179e74d6610afd1a3a3a97e56f808b664c98976d1a55441c8e643f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:E6WMCUOZYGYAYAO6KJIUSFWKKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"R Boundedness, Maximal Regularity and Free Boundary Problems for the Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yoshihiro Shibata","submitted_at":"2019-05-30T07:50:07Z","abstract_excerpt":"In this lecture note, we study free boundary problems for the Navier-Stokes equations with and without surface tension. The local well-posedness, the global well-posedness, and asymptotics of solutions as time goes to infinity are studied in the Lp in time and Lq in space framework. The tool in proving the local well-posedness is the maximal Lp-Lq regularity for the Stokes equations with non-homogeneous free boundary conditions. The approach here of proving the maximal Lp-Lq regularity is based on the R bounded solution operators of the generalized resolvent problem for the Stokes equations wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12900","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPOM6ej4rX4khDMke8mh17cqGh79DK45mc6bXJzi4Lc/1bvXHoNDgNX/WXLAjYQd2ROWFHVJLFliruN80fZaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:24:04.558882Z"},"content_sha256":"4966dfbb72faa277015661575f2780c693b3a91fd9fd184b531e73e1e963086c","schema_version":"1.0","event_id":"sha256:4966dfbb72faa277015661575f2780c693b3a91fd9fd184b531e73e1e963086c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/bundle.json","state_url":"https://pith.science/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T21:24:04Z","links":{"resolver":"https://pith.science/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA","bundle":"https://pith.science/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/bundle.json","state":"https://pith.science/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6WMCUOZYGYAYAO6KJIUSFWKKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E6WMCUOZYGYAYAO6KJIUSFWKKA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"89792cf4dc09a0feda929ab1b97395fb16fa2c3381f8e044049283be04cda361","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-30T07:50:07Z","title_canon_sha256":"6a5a328585a17567aa0cf5f8b2fb81c3096f6c16f4857db98bafe3b6d2d8b352"},"schema_version":"1.0","source":{"id":"1905.12900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12900","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12900v1","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12900","created_at":"2026-05-17T23:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"E6WMCUOZYGYA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E6WMCUOZYGYAYAO6","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E6WMCUOZ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:4966dfbb72faa277015661575f2780c693b3a91fd9fd184b531e73e1e963086c","target":"graph","created_at":"2026-05-17T23:44:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this lecture note, we study free boundary problems for the Navier-Stokes equations with and without surface tension. The local well-posedness, the global well-posedness, and asymptotics of solutions as time goes to infinity are studied in the Lp in time and Lq in space framework. The tool in proving the local well-posedness is the maximal Lp-Lq regularity for the Stokes equations with non-homogeneous free boundary conditions. The approach here of proving the maximal Lp-Lq regularity is based on the R bounded solution operators of the generalized resolvent problem for the Stokes equations wi","authors_text":"Yoshihiro Shibata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-30T07:50:07Z","title":"R Boundedness, Maximal Regularity and Free Boundary Problems for the Navier-Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12900","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:22a949ff8179e74d6610afd1a3a3a97e56f808b664c98976d1a55441c8e643f8","target":"record","created_at":"2026-05-17T23:44:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"89792cf4dc09a0feda929ab1b97395fb16fa2c3381f8e044049283be04cda361","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-30T07:50:07Z","title_canon_sha256":"6a5a328585a17567aa0cf5f8b2fb81c3096f6c16f4857db98bafe3b6d2d8b352"},"schema_version":"1.0","source":{"id":"1905.12900","kind":"arxiv","version":1}},"canonical_sha256":"27acc151d9c1b00c01de52514916ca5039aa532c7ad815aed84d31fe1b32041d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27acc151d9c1b00c01de52514916ca5039aa532c7ad815aed84d31fe1b32041d","first_computed_at":"2026-05-17T23:44:39.380424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:39.380424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JTp4/I4jXkTn8faA0hgDY1SxxxkugxKwDbve19+/XF9/el5qIkbl1A7tpzH21Z4YhFFshzTZoxvnC5fzDRNGDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:39.380987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.12900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22a949ff8179e74d6610afd1a3a3a97e56f808b664c98976d1a55441c8e643f8","sha256:4966dfbb72faa277015661575f2780c693b3a91fd9fd184b531e73e1e963086c"],"state_sha256":"ca4f8179b74fd5a8f85cdd09d3789a38735410953ba9cd7beee70a3ceffc0934"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5EVZBfB3Wm0oDvqvo+TgeBlWOx4IFd7toe2MXppfUagnu5UseJlPcGAe4/u0A7QsEzFLxb7YWI7J30Br4juCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:24:04.560925Z","bundle_sha256":"0bb4a2c0a1f38be812dd8e6db3607c2ded2cbf8cb028e34f1c651710c24fdf11"}}