{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:C4Q5XPABLUSUUM54Y3ZHG2LVEV","short_pith_number":"pith:C4Q5XPAB","schema_version":"1.0","canonical_sha256":"1721dbbc015d254a33bcc6f2736975257959a6a0df30facf81599abacf5ad727","source":{"kind":"arxiv","id":"1212.5980","version":1},"attestation_state":"computed","paper":{"title":"Global well-posedness of the compressible bipolar Euler-Maxwell system in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Wang, Zhong Tan","submitted_at":"2012-12-25T01:15:32Z","abstract_excerpt":"We first construct the global unique solution by assuming that the initial data is small in the H^3 norm but its higher order derivatives could be large. If further the initial data belongs to \\Dot{H}^{-s} (0\\le s<3/2) or \\dot{B}_{2,\\infty}^{-s} (0< s\\le3/2), we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the L^p-L^2 (1\\le p\\le 2) type of the decay rates follow without requiring the smallness for L^p norm of initial data. In particular, the decay rate for the difference of densities could reach to (1+t)^{-13/4} in L^2 norm."},"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":"1212.5980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-25T01:15:32Z","cross_cats_sorted":[],"title_canon_sha256":"1b6103763133297953f2874c242b92de661963f33ae8e2c6e7996e52da450812","abstract_canon_sha256":"698764d003e581500cf5e9a6ac42122b86169a17f20a6deb3d37326814ef0f05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:50.905494Z","signature_b64":"ZSnuAFk9U6DpFuM4KvK2ytRVgiAo77Bp/HJy2pz1PAqJeyLmbZ2Q3//sTtQR9X2GNrt2ALqNp6Lvus2Nrl25Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1721dbbc015d254a33bcc6f2736975257959a6a0df30facf81599abacf5ad727","last_reissued_at":"2026-05-18T03:37:50.904696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:50.904696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global well-posedness of the compressible bipolar Euler-Maxwell system in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Wang, Zhong Tan","submitted_at":"2012-12-25T01:15:32Z","abstract_excerpt":"We first construct the global unique solution by assuming that the initial data is small in the H^3 norm but its higher order derivatives could be large. If further the initial data belongs to \\Dot{H}^{-s} (0\\le s<3/2) or \\dot{B}_{2,\\infty}^{-s} (0< s\\le3/2), we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the L^p-L^2 (1\\le p\\le 2) type of the decay rates follow without requiring the smallness for L^p norm of initial data. In particular, the decay rate for the difference of densities could reach to (1+t)^{-13/4} in L^2 norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5980","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":"1212.5980","created_at":"2026-05-18T03:37:50.904832+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5980v1","created_at":"2026-05-18T03:37:50.904832+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5980","created_at":"2026-05-18T03:37:50.904832+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4Q5XPABLUSU","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4Q5XPABLUSUUM54","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4Q5XPAB","created_at":"2026-05-18T12:27:01.376967+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/C4Q5XPABLUSUUM54Y3ZHG2LVEV","json":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV.json","graph_json":"https://pith.science/api/pith-number/C4Q5XPABLUSUUM54Y3ZHG2LVEV/graph.json","events_json":"https://pith.science/api/pith-number/C4Q5XPABLUSUUM54Y3ZHG2LVEV/events.json","paper":"https://pith.science/paper/C4Q5XPAB"},"agent_actions":{"view_html":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV","download_json":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV.json","view_paper":"https://pith.science/paper/C4Q5XPAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5980&json=true","fetch_graph":"https://pith.science/api/pith-number/C4Q5XPABLUSUUM54Y3ZHG2LVEV/graph.json","fetch_events":"https://pith.science/api/pith-number/C4Q5XPABLUSUUM54Y3ZHG2LVEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV/action/storage_attestation","attest_author":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV/action/author_attestation","sign_citation":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV/action/citation_signature","submit_replication":"https://pith.science/pith/C4Q5XPABLUSUUM54Y3ZHG2LVEV/action/replication_record"}},"created_at":"2026-05-18T03:37:50.904832+00:00","updated_at":"2026-05-18T03:37:50.904832+00:00"}