{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CYD5I6NTUOAQRW3QOL46UTZOS4","short_pith_number":"pith:CYD5I6NT","schema_version":"1.0","canonical_sha256":"1607d479b3a38108db7072f9ea4f2e971646425f98c10344be538fab9e1f577e","source":{"kind":"arxiv","id":"1410.8636","version":1},"attestation_state":"computed","paper":{"title":"On the Decay and Stability of Global Solutions to the 3D Inhomogeneous MHD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jigen Peng, Junxiong Jia, Kexue Li","submitted_at":"2014-10-31T04:43:00Z","abstract_excerpt":"In this paper, we investigative the large time decay and stability to any given global smooth solutions of the $3$D incompressible inhomogeneous MHD systems. We proved that given a solution $(a, u, B)$ of (\\ref{mhd_a}), the velocity field and magnetic field decay to $0$ with an explicit rate, for $u$ which coincide with incompressible inhomogeneous Navier-Stokes equations \\cite{zhangping}. In particular, we give the decay rate of higher order derivatives of $u$ and $B$ which is useful to prove our main stability result. For a large solutions of (\\ref{mhd_a}) denoted by $(a, u, B)$, we proved t"},"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":"1410.8636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-31T04:43:00Z","cross_cats_sorted":[],"title_canon_sha256":"f7427cadffe1e256501c89a9e61bb8941109c4030e372f630d5247fc0b35225f","abstract_canon_sha256":"181de2bc38171c8833a98ec600bc6dec3a43b6f339e2e92c3cbb6d54c26d7b4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:54.050744Z","signature_b64":"jHpVs/LpVKgCcg0fCKQwclBSozWwyaa6eGeSX2y6J680gshbWVzqLEG21dIolcdvaqCNyWVsZe/h2FRAzZP+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1607d479b3a38108db7072f9ea4f2e971646425f98c10344be538fab9e1f577e","last_reissued_at":"2026-05-18T02:38:54.050339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:54.050339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Decay and Stability of Global Solutions to the 3D Inhomogeneous MHD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jigen Peng, Junxiong Jia, Kexue Li","submitted_at":"2014-10-31T04:43:00Z","abstract_excerpt":"In this paper, we investigative the large time decay and stability to any given global smooth solutions of the $3$D incompressible inhomogeneous MHD systems. We proved that given a solution $(a, u, B)$ of (\\ref{mhd_a}), the velocity field and magnetic field decay to $0$ with an explicit rate, for $u$ which coincide with incompressible inhomogeneous Navier-Stokes equations \\cite{zhangping}. In particular, we give the decay rate of higher order derivatives of $u$ and $B$ which is useful to prove our main stability result. For a large solutions of (\\ref{mhd_a}) denoted by $(a, u, B)$, we proved t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8636","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":"1410.8636","created_at":"2026-05-18T02:38:54.050397+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8636v1","created_at":"2026-05-18T02:38:54.050397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8636","created_at":"2026-05-18T02:38:54.050397+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYD5I6NTUOAQ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYD5I6NTUOAQRW3Q","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYD5I6NT","created_at":"2026-05-18T12:28:25.294606+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/CYD5I6NTUOAQRW3QOL46UTZOS4","json":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4.json","graph_json":"https://pith.science/api/pith-number/CYD5I6NTUOAQRW3QOL46UTZOS4/graph.json","events_json":"https://pith.science/api/pith-number/CYD5I6NTUOAQRW3QOL46UTZOS4/events.json","paper":"https://pith.science/paper/CYD5I6NT"},"agent_actions":{"view_html":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4","download_json":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4.json","view_paper":"https://pith.science/paper/CYD5I6NT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8636&json=true","fetch_graph":"https://pith.science/api/pith-number/CYD5I6NTUOAQRW3QOL46UTZOS4/graph.json","fetch_events":"https://pith.science/api/pith-number/CYD5I6NTUOAQRW3QOL46UTZOS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4/action/storage_attestation","attest_author":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4/action/author_attestation","sign_citation":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4/action/citation_signature","submit_replication":"https://pith.science/pith/CYD5I6NTUOAQRW3QOL46UTZOS4/action/replication_record"}},"created_at":"2026-05-18T02:38:54.050397+00:00","updated_at":"2026-05-18T02:38:54.050397+00:00"}