{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2GSTPHIUTLCPKLUNZZFCMUKQHA","short_pith_number":"pith:2GSTPHIU","schema_version":"1.0","canonical_sha256":"d1a5379d149ac4f52e8dce4a265150380a4356d6bdb7c24d8cb5e05b87b0771a","source":{"kind":"arxiv","id":"1703.03177","version":1},"attestation_state":"computed","paper":{"title":"Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bohdan Maslowski, Dominic Breit, Eduard Feireisl, Martina Hofmanova","submitted_at":"2017-03-09T08:40:59Z","abstract_excerpt":"We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue--Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. In contrast with the deterministic case, where related results were obtained only under rather restrictive consti"},"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":"1703.03177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-09T08:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"2842e2c07c7f69452aac7ba4dd67ffedc8ae1e159de4935baf142096adcb6611","abstract_canon_sha256":"d64fcbfd6f6b238084fb65e5d88d05ae9453727b11162a6d9d4679cbadfc2d55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:01.223136Z","signature_b64":"/CaCGBf6RU7mmI/10PhhrkjpmDgpX6WSP0VbmTpMpvU0GEZHPmsOR2yErhtjCBrXtHVisPKIkPlZ6K9lo3x4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1a5379d149ac4f52e8dce4a265150380a4356d6bdb7c24d8cb5e05b87b0771a","last_reissued_at":"2026-05-18T00:49:01.222507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:01.222507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bohdan Maslowski, Dominic Breit, Eduard Feireisl, Martina Hofmanova","submitted_at":"2017-03-09T08:40:59Z","abstract_excerpt":"We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue--Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. In contrast with the deterministic case, where related results were obtained only under rather restrictive consti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03177","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":"1703.03177","created_at":"2026-05-18T00:49:01.222625+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03177v1","created_at":"2026-05-18T00:49:01.222625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03177","created_at":"2026-05-18T00:49:01.222625+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GSTPHIUTLCP","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GSTPHIUTLCPKLUN","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GSTPHIU","created_at":"2026-05-18T12:30:55.937587+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/2GSTPHIUTLCPKLUNZZFCMUKQHA","json":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA.json","graph_json":"https://pith.science/api/pith-number/2GSTPHIUTLCPKLUNZZFCMUKQHA/graph.json","events_json":"https://pith.science/api/pith-number/2GSTPHIUTLCPKLUNZZFCMUKQHA/events.json","paper":"https://pith.science/paper/2GSTPHIU"},"agent_actions":{"view_html":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA","download_json":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA.json","view_paper":"https://pith.science/paper/2GSTPHIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03177&json=true","fetch_graph":"https://pith.science/api/pith-number/2GSTPHIUTLCPKLUNZZFCMUKQHA/graph.json","fetch_events":"https://pith.science/api/pith-number/2GSTPHIUTLCPKLUNZZFCMUKQHA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA/action/storage_attestation","attest_author":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA/action/author_attestation","sign_citation":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA/action/citation_signature","submit_replication":"https://pith.science/pith/2GSTPHIUTLCPKLUNZZFCMUKQHA/action/replication_record"}},"created_at":"2026-05-18T00:49:01.222625+00:00","updated_at":"2026-05-18T00:49:01.222625+00:00"}