{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5R7X42JVRH6CFUBHXIXCEKKSHO","short_pith_number":"pith:5R7X42JV","schema_version":"1.0","canonical_sha256":"ec7f7e693589fc22d027ba2e2229523bbc92a177cfcb2d981f3b9c6f16834893","source":{"kind":"arxiv","id":"1906.09119","version":1},"attestation_state":"computed","paper":{"title":"Optimal decay for the compressible MHD equations in the critical regularity framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiru Wang, Qunyi Bie, Zheng-an Yao","submitted_at":"2019-06-20T12:04:26Z","abstract_excerpt":"In this paper, we study the large time behavior of solutions to the compressible magnetohydrodynamic equations in the $L^p$-type critical Besov spaces. Precisely, we show that if the initial data in the low frequencies additionally belong to some Besov space $\\dot{B}_{2,\\infty}^{-\\sigma_1}$ with $\\sigma_1\\in (1-N/2, 2N/p-N/2]$, then the $\\dot{B}_{p,1}^0$ norm of the critical global solutions presents the optimal decay $t^{-\\frac{N}{2}(\\frac{1}{2}-\\frac{1}{p})-\\frac{\\sigma_1}{2}}$ for $t\\rightarrow+\\infty$. The pure energy argument without the spectral analysis is performed, which allows us to "},"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":"1906.09119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-20T12:04:26Z","cross_cats_sorted":[],"title_canon_sha256":"24a02c7cd861803a910e7db20a1d9fac8be19bb065b1f6761331b49302f56beb","abstract_canon_sha256":"d1c245a2d36510ab5787ae2c992f4ed55e03b6c475bc60ce6da4277709b89c14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:44.474762Z","signature_b64":"9+dU89up80Jollz/Ec3ifNBWlJGvCpjWGAvMcMZLV1E2BrDi0umHP+f2qTkfLFULXyA5Fqohe3TjmmUwDPHDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec7f7e693589fc22d027ba2e2229523bbc92a177cfcb2d981f3b9c6f16834893","last_reissued_at":"2026-05-17T23:42:44.474213Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:44.474213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal decay for the compressible MHD equations in the critical regularity framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qiru Wang, Qunyi Bie, Zheng-an Yao","submitted_at":"2019-06-20T12:04:26Z","abstract_excerpt":"In this paper, we study the large time behavior of solutions to the compressible magnetohydrodynamic equations in the $L^p$-type critical Besov spaces. Precisely, we show that if the initial data in the low frequencies additionally belong to some Besov space $\\dot{B}_{2,\\infty}^{-\\sigma_1}$ with $\\sigma_1\\in (1-N/2, 2N/p-N/2]$, then the $\\dot{B}_{p,1}^0$ norm of the critical global solutions presents the optimal decay $t^{-\\frac{N}{2}(\\frac{1}{2}-\\frac{1}{p})-\\frac{\\sigma_1}{2}}$ for $t\\rightarrow+\\infty$. The pure energy argument without the spectral analysis is performed, which allows us to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09119","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":"1906.09119","created_at":"2026-05-17T23:42:44.474287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.09119v1","created_at":"2026-05-17T23:42:44.474287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09119","created_at":"2026-05-17T23:42:44.474287+00:00"},{"alias_kind":"pith_short_12","alias_value":"5R7X42JVRH6C","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5R7X42JVRH6CFUBH","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5R7X42JV","created_at":"2026-05-18T12:33:10.108867+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/5R7X42JVRH6CFUBHXIXCEKKSHO","json":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO.json","graph_json":"https://pith.science/api/pith-number/5R7X42JVRH6CFUBHXIXCEKKSHO/graph.json","events_json":"https://pith.science/api/pith-number/5R7X42JVRH6CFUBHXIXCEKKSHO/events.json","paper":"https://pith.science/paper/5R7X42JV"},"agent_actions":{"view_html":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO","download_json":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO.json","view_paper":"https://pith.science/paper/5R7X42JV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.09119&json=true","fetch_graph":"https://pith.science/api/pith-number/5R7X42JVRH6CFUBHXIXCEKKSHO/graph.json","fetch_events":"https://pith.science/api/pith-number/5R7X42JVRH6CFUBHXIXCEKKSHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO/action/storage_attestation","attest_author":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO/action/author_attestation","sign_citation":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO/action/citation_signature","submit_replication":"https://pith.science/pith/5R7X42JVRH6CFUBHXIXCEKKSHO/action/replication_record"}},"created_at":"2026-05-17T23:42:44.474287+00:00","updated_at":"2026-05-17T23:42:44.474287+00:00"}