{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H3K373V4A2HJUPWJVPAJDXTO3Z","short_pith_number":"pith:H3K373V4","schema_version":"1.0","canonical_sha256":"3ed5bfeebc068e9a3ec9abc091de6ede6cb9798f555c643095890031a754055f","source":{"kind":"arxiv","id":"1507.02468","version":1},"attestation_state":"computed","paper":{"title":"Global well-posedness for axisymmetric MHD system with only vertical viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan Yu, Quansen Jiu, Xiaoxin Zheng","submitted_at":"2015-07-09T11:49:22Z","abstract_excerpt":"In this paper, we are concerned with the global well-posedness of a tri-dimensional MHD system with only vertical viscosity in velocity equation for the large axisymmetric initial data. By making good use of the axisymmetric structure of flow and the maximal smoothing effect of vertical diffusion, we show that $\\displaystyle\\sup_{2\\leq p<\\infty}\\int_0^t\\frac{\\|\\partial_{z}u(\\tau)\\|_{L^p}^{2}}{p^{3/4}}\\,\\mathrm{d}\\tau<\\infty$. With this regularity for the vertical first derivative of velocity vector field, we further establish losing estimates for the anisotropy tri-dimensional MHD system to ge"},"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":"1507.02468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-09T11:49:22Z","cross_cats_sorted":[],"title_canon_sha256":"bf1ad272e32f6b96f6a5beac69de891ed2705aacd7085e0456d63fc0009aa842","abstract_canon_sha256":"f2b96cfbcff0be8b50223a3fdb77191ffb56b771350adec0727d1346330ecdf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:06.654000Z","signature_b64":"agJ971pbXtc3ibszUMpwuCk7GtpTWi7pr2VoIE0pabz731+bsVfWt9AHnD6XOFpZS6ZnChwVvgYX1WuGq9JaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ed5bfeebc068e9a3ec9abc091de6ede6cb9798f555c643095890031a754055f","last_reissued_at":"2026-05-18T01:37:06.653398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:06.653398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global well-posedness for axisymmetric MHD system with only vertical viscosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan Yu, Quansen Jiu, Xiaoxin Zheng","submitted_at":"2015-07-09T11:49:22Z","abstract_excerpt":"In this paper, we are concerned with the global well-posedness of a tri-dimensional MHD system with only vertical viscosity in velocity equation for the large axisymmetric initial data. By making good use of the axisymmetric structure of flow and the maximal smoothing effect of vertical diffusion, we show that $\\displaystyle\\sup_{2\\leq p<\\infty}\\int_0^t\\frac{\\|\\partial_{z}u(\\tau)\\|_{L^p}^{2}}{p^{3/4}}\\,\\mathrm{d}\\tau<\\infty$. With this regularity for the vertical first derivative of velocity vector field, we further establish losing estimates for the anisotropy tri-dimensional MHD system to ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02468","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":"1507.02468","created_at":"2026-05-18T01:37:06.653494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02468v1","created_at":"2026-05-18T01:37:06.653494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02468","created_at":"2026-05-18T01:37:06.653494+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3K373V4A2HJ","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3K373V4A2HJUPWJ","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3K373V4","created_at":"2026-05-18T12:29:22.688609+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/H3K373V4A2HJUPWJVPAJDXTO3Z","json":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z.json","graph_json":"https://pith.science/api/pith-number/H3K373V4A2HJUPWJVPAJDXTO3Z/graph.json","events_json":"https://pith.science/api/pith-number/H3K373V4A2HJUPWJVPAJDXTO3Z/events.json","paper":"https://pith.science/paper/H3K373V4"},"agent_actions":{"view_html":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z","download_json":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z.json","view_paper":"https://pith.science/paper/H3K373V4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02468&json=true","fetch_graph":"https://pith.science/api/pith-number/H3K373V4A2HJUPWJVPAJDXTO3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/H3K373V4A2HJUPWJVPAJDXTO3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z/action/storage_attestation","attest_author":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z/action/author_attestation","sign_citation":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z/action/citation_signature","submit_replication":"https://pith.science/pith/H3K373V4A2HJUPWJVPAJDXTO3Z/action/replication_record"}},"created_at":"2026-05-18T01:37:06.653494+00:00","updated_at":"2026-05-18T01:37:06.653494+00:00"}