{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ZT2NJPJIWDJHUOTUY56JPEER4R","short_pith_number":"pith:ZT2NJPJI","schema_version":"1.0","canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","source":{"kind":"arxiv","id":"2401.12548","version":1},"attestation_state":"computed","paper":{"title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Niklas Knobel","submitted_at":"2024-01-23T08:13:08Z","abstract_excerpt":"In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $\\nu$ is larger than resistivity $\\kappa$, $\\nu\\ge \\kappa>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $\\kappa\\le \\nu^3$ this system exhibits instability, which leads to norm inflation of size $\\nu \\kappa^{-\\frac 1 3 }$."},"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":"2401.12548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f4a46f6d4881e3d631147c8b3259c42a2ab9e4357a2174a49c7e4ab50f0625cf","abstract_canon_sha256":"11a365dc1bad49101a69fd9c4aad0129c58af4c34a9a819b0c744031aca832a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:36:32.341764Z","signature_b64":"ix1RdH/X+jl8+GwCKJZz+lr7mBMH0fEptRJ06rGTSo8QB3Agg73V3Jd68x054O/PG62s8KmT64WCJRpZEl8FBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","last_reissued_at":"2026-07-05T07:36:32.341326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:36:32.341326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Niklas Knobel","submitted_at":"2024-01-23T08:13:08Z","abstract_excerpt":"In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $\\nu$ is larger than resistivity $\\kappa$, $\\nu\\ge \\kappa>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $\\kappa\\le \\nu^3$ this system exhibits instability, which leads to norm inflation of size $\\nu \\kappa^{-\\frac 1 3 }$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12548","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.12548/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2401.12548","created_at":"2026-07-05T07:36:32.341382+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.12548v1","created_at":"2026-07-05T07:36:32.341382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12548","created_at":"2026-07-05T07:36:32.341382+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZT2NJPJIWDJH","created_at":"2026-07-05T07:36:32.341382+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZT2NJPJIWDJHUOTU","created_at":"2026-07-05T07:36:32.341382+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZT2NJPJI","created_at":"2026-07-05T07:36:32.341382+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23391","citing_title":"Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R","json":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R.json","graph_json":"https://pith.science/api/pith-number/ZT2NJPJIWDJHUOTUY56JPEER4R/graph.json","events_json":"https://pith.science/api/pith-number/ZT2NJPJIWDJHUOTUY56JPEER4R/events.json","paper":"https://pith.science/paper/ZT2NJPJI"},"agent_actions":{"view_html":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R","download_json":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R.json","view_paper":"https://pith.science/paper/ZT2NJPJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.12548&json=true","fetch_graph":"https://pith.science/api/pith-number/ZT2NJPJIWDJHUOTUY56JPEER4R/graph.json","fetch_events":"https://pith.science/api/pith-number/ZT2NJPJIWDJHUOTUY56JPEER4R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/action/storage_attestation","attest_author":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/action/author_attestation","sign_citation":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/action/citation_signature","submit_replication":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/action/replication_record"}},"created_at":"2026-07-05T07:36:32.341382+00:00","updated_at":"2026-07-05T07:36:32.341382+00:00"}