{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6JTHUXBE7UXMOXVJQMABLASFBY","short_pith_number":"pith:6JTHUXBE","schema_version":"1.0","canonical_sha256":"f2667a5c24fd2ec75ea983001582450e2ea1b16c4b6342e488e051ae724f8ce6","source":{"kind":"arxiv","id":"1409.5665","version":1},"attestation_state":"computed","paper":{"title":"Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yu Mei","submitted_at":"2014-09-19T14:17:46Z","abstract_excerpt":"In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\\mu=const.$ and $\\lambda=\\rho^\\beta,~\\beta>1$ (Va\\v{i}gant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus $\\mathbb{T}^2$ and the whole space $\\mathbb{R}^2$ (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Va\\v{i}gant-Kazhikhov model of compressible Navier-Stokes."},"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":"1409.5665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-19T14:17:46Z","cross_cats_sorted":[],"title_canon_sha256":"3b6e31f40e800eaab70025b166f823bfa0a9567ec1782b930598ef2c5136609b","abstract_canon_sha256":"2163122ef9857e3068001a61182fe7db3a5fe5de3e97a476ecf3d7f6f332af24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:26.632140Z","signature_b64":"edwBU1bZPB5aUbTzX3ktdGgMVDxguK3Q5ubf2pQhR3wQODeCz/1NgAZf1XTWkc8/a2ATl+9bUxSb2m7qZnNyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2667a5c24fd2ec75ea983001582450e2ea1b16c4b6342e488e051ae724f8ce6","last_reissued_at":"2026-05-18T02:42:26.631448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:26.631448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yu Mei","submitted_at":"2014-09-19T14:17:46Z","abstract_excerpt":"In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\\mu=const.$ and $\\lambda=\\rho^\\beta,~\\beta>1$ (Va\\v{i}gant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus $\\mathbb{T}^2$ and the whole space $\\mathbb{R}^2$ (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Va\\v{i}gant-Kazhikhov model of compressible Navier-Stokes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5665","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":"1409.5665","created_at":"2026-05-18T02:42:26.631553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5665v1","created_at":"2026-05-18T02:42:26.631553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5665","created_at":"2026-05-18T02:42:26.631553+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JTHUXBE7UXM","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JTHUXBE7UXMOXVJ","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JTHUXBE","created_at":"2026-05-18T12:28:16.859392+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/6JTHUXBE7UXMOXVJQMABLASFBY","json":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY.json","graph_json":"https://pith.science/api/pith-number/6JTHUXBE7UXMOXVJQMABLASFBY/graph.json","events_json":"https://pith.science/api/pith-number/6JTHUXBE7UXMOXVJQMABLASFBY/events.json","paper":"https://pith.science/paper/6JTHUXBE"},"agent_actions":{"view_html":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY","download_json":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY.json","view_paper":"https://pith.science/paper/6JTHUXBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5665&json=true","fetch_graph":"https://pith.science/api/pith-number/6JTHUXBE7UXMOXVJQMABLASFBY/graph.json","fetch_events":"https://pith.science/api/pith-number/6JTHUXBE7UXMOXVJQMABLASFBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY/action/storage_attestation","attest_author":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY/action/author_attestation","sign_citation":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY/action/citation_signature","submit_replication":"https://pith.science/pith/6JTHUXBE7UXMOXVJQMABLASFBY/action/replication_record"}},"created_at":"2026-05-18T02:42:26.631553+00:00","updated_at":"2026-05-18T02:42:26.631553+00:00"}