{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VUK5Q7EF7ADP4CB4QZCZM7JBQ6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0a1b6194d6a1e0af20230c5fdddba24cb67d49af5e702cb6fab31417aeaf99d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-20T08:12:02Z","title_canon_sha256":"64d71282ae635993e35f2f34a592478bf7628f5ad7c15cd63d9487ec5a28ac9f"},"schema_version":"1.0","source":{"id":"1402.4923","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4923","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4923v3","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4923","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"pith_short_12","alias_value":"VUK5Q7EF7ADP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VUK5Q7EF7ADP4CB4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VUK5Q7EF","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:d36e2ee16dd0723401eb6c8eac5e4fdfee954dd72c01f0e6d7b6cad625a19ad5","target":"graph","created_at":"2026-05-18T02:32:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider the Cauchy problem for 2D viscous shallow water system in Besov spaces. We firstly prove the local well-posedness of this problem in $B^s_{p,r}(\\mathbb{R}^2)$, $s>max\\{1,\\frac{2}{p}\\}$, $1\\leq p,r\\leq \\infty$ by using the Littlewood-Paley theory, the Bony decomposition and the theories of transport equations and transport diffusion equations. Then we can prove the global existence of the system with small enough initial data in $B^s_{p,r}(\\mathbb{R}^2)$, $1\\leq p\\leq2$, $1\\leq r<\\infty$ and $s>\\frac{2}{p}$. Our obtained results generalize and cover the recent results ","authors_text":"Yanan Liu, Zhaoyang Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-20T08:12:02Z","title":"Well-posedness and global existence of 2D viscous shallow water system in Besov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4923","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:734aea3ed26b3a7349469681812fc80c40294a5a19e6c0a7e90792a196b4e68b","target":"record","created_at":"2026-05-18T02:32:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0a1b6194d6a1e0af20230c5fdddba24cb67d49af5e702cb6fab31417aeaf99d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-20T08:12:02Z","title_canon_sha256":"64d71282ae635993e35f2f34a592478bf7628f5ad7c15cd63d9487ec5a28ac9f"},"schema_version":"1.0","source":{"id":"1402.4923","kind":"arxiv","version":3}},"canonical_sha256":"ad15d87c85f806fe083c8645967d2187880ef80392613cd7c9a5e9ae651d0179","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad15d87c85f806fe083c8645967d2187880ef80392613cd7c9a5e9ae651d0179","first_computed_at":"2026-05-18T02:32:38.899109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:38.899109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rbl1hFI0qCQmmpEgA5yALNzW6nM61R7QPEH0V/n7gUqnd9i2H9cSaHFQzwxoLJCz2bHNQbXyons2+ONSBWp2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:38.899483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4923","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734aea3ed26b3a7349469681812fc80c40294a5a19e6c0a7e90792a196b4e68b","sha256:d36e2ee16dd0723401eb6c8eac5e4fdfee954dd72c01f0e6d7b6cad625a19ad5"],"state_sha256":"7a49707342e2ff9f0fc103ad48cb6c4a43eb9e4c5f6be7db2ba08c155e2a505c"}