{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HMKSZZZNRM3TPXEF2L74C752ER","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":"c15b133260c4154455733fdb8e25194005a3f744d4c5dd50f2b64490a28169c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-08T08:07:41Z","title_canon_sha256":"7430d8ee07bfe8b5d767202093dc8d8551395e36a9462f1e52fe29e3ecea654b"},"schema_version":"1.0","source":{"id":"1106.1515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1515","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1515v2","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1515","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"HMKSZZZNRM3T","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMKSZZZNRM3TPXEF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMKSZZZN","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:8bce6c175b029ac2199bd338f3ce38f2ba74c07704167fc564c935f93a684b84","target":"graph","created_at":"2026-05-18T04:19:42Z","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 paper we prove Liouville type result for the stationary solutions to the compressible Navier-Stokes-Poisson equations(NSP) and the compressible Navier-Stokes equations(NS) in $\\Bbb R^N$, $N\\geq 2$. Assuming suitable integrability and the uniform boundedness conditions for the solutions we are led to the conclusion that $v=0$. In the case of (NS) we deduce that the similar integrability conditions imply $v=0$ and $\\rho=$constant on $\\Bbb R^N$. This shows that if we impose the the non-vacuum boundary condition at spatial infinity for (NS), $v\\to 0$ and $\\rho\\to \\rho_\\infty >0$, then $v=0","authors_text":"Dongho Chae","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-08T08:07:41Z","title":"On the Liouville type theorem for stationary compressible Navier-Stokes-Poisson equations in $\\Bbb R^N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1515","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":"sha256:9045050775a2c5467e5fba9f18a75b43e5cc4616a2e452a33c9aa8ccabc83ea2","target":"record","created_at":"2026-05-18T04:19:42Z","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":"c15b133260c4154455733fdb8e25194005a3f744d4c5dd50f2b64490a28169c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-08T08:07:41Z","title_canon_sha256":"7430d8ee07bfe8b5d767202093dc8d8551395e36a9462f1e52fe29e3ecea654b"},"schema_version":"1.0","source":{"id":"1106.1515","kind":"arxiv","version":2}},"canonical_sha256":"3b152ce72d8b3737dc85d2ffc17fba244566ff98fa9f92b16ca176fdb94dab14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b152ce72d8b3737dc85d2ffc17fba244566ff98fa9f92b16ca176fdb94dab14","first_computed_at":"2026-05-18T04:19:42.863578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:42.863578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qLhLzQA1frTKJ6X4KyGKvsfXIeW//lA24uzlB6cQOfr+tQ7FZDrdgGjovRw3ovDPDJDfvvu2Q2+yKPCENeUeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:42.864228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9045050775a2c5467e5fba9f18a75b43e5cc4616a2e452a33c9aa8ccabc83ea2","sha256:8bce6c175b029ac2199bd338f3ce38f2ba74c07704167fc564c935f93a684b84"],"state_sha256":"0aa1f940d4f6a36e056e912e27c69380a2c7fbc5c4512897c7920bf2156758f6"}