{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z2ZSYJIDMWPMRLZJDM3XRVBLO3","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":"9e289247c587b4fcbe19d4056e8a8b105f8b29141ecac8067a8c453eff27064c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2009-07-27T03:23:10Z","title_canon_sha256":"3990f9825c098eb04bc01bd27dacbca80db641b4cc3092fde53a04fbbae8a06e"},"schema_version":"1.0","source":{"id":"0907.4540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4540","created_at":"2026-07-04T17:31:17Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4540v2","created_at":"2026-07-04T17:31:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4540","created_at":"2026-07-04T17:31:17Z"},{"alias_kind":"pith_short_12","alias_value":"Z2ZSYJIDMWPM","created_at":"2026-07-04T17:31:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z2ZSYJIDMWPMRLZJ","created_at":"2026-07-04T17:31:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z2ZSYJID","created_at":"2026-07-04T17:31:17Z"}],"graph_snapshots":[{"event_id":"sha256:05515ef810ff5440711d5ec845aee94566dd0a6b39b0284e81e625c166127bd7","target":"graph","created_at":"2026-07-04T17:31:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0907.4540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Cannone \\cite{Cannone} proved the global well-posedness of the incompressible Navier-Stokes equations for a class of highly oscillating data. In this paper, we prove the global well-posedness for the compressible Navier-Stokes equations in the critical functional framework with the initial data close to a stable equilibrium. Especially, this result allows us to construct global solutions for the highly oscillating initial velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms.","authors_text":"Changxing Miao, Qionglei Chen, Zhifei Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2009-07-27T03:23:10Z","title":"Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4540","kind":"arxiv","version":2},"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":"sha256:80c4149f7b5128a68f97051df62adf5c839c69075dce0be5641c777e9fc0972c","target":"record","created_at":"2026-07-04T17:31:17Z","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":"9e289247c587b4fcbe19d4056e8a8b105f8b29141ecac8067a8c453eff27064c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2009-07-27T03:23:10Z","title_canon_sha256":"3990f9825c098eb04bc01bd27dacbca80db641b4cc3092fde53a04fbbae8a06e"},"schema_version":"1.0","source":{"id":"0907.4540","kind":"arxiv","version":2}},"canonical_sha256":"ceb32c2503659ec8af291b3778d42b76e402a7d4b5c6c334cd5dfbf0e85da993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceb32c2503659ec8af291b3778d42b76e402a7d4b5c6c334cd5dfbf0e85da993","first_computed_at":"2026-07-04T17:31:17.101036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:31:17.101036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hFEQKTzxX/3Ugb/FRlZf2RXYbgt8IXT9CO30j7au9IgP9od7T7zOoZrO3UGHyv5g1frKQygays8PLKkJG04/AQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:31:17.101493Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80c4149f7b5128a68f97051df62adf5c839c69075dce0be5641c777e9fc0972c","sha256:05515ef810ff5440711d5ec845aee94566dd0a6b39b0284e81e625c166127bd7"],"state_sha256":"fbe9076eebb1d499c2b5362009b436d8095a15f3df4c2d60d284ec5d132791eb"}