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Let $T>0$ be the horizontal period of the channel and $\\alpha={2\\pi\\over T}$ be the wave number. We obtain a sharp region $O$ in the whole $(\\alpha,\\beta)$ half-plane such that non-parallel steadily traveling waves do not exist for $(\\alpha,\\beta)\\in O$ and such traveling waves exist for $(\\alpha,\\beta)$ in the remaining regions, near Couette fl"},"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":"2202.05708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-02-11T15:43:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6fc858ddaf2fa131f3dd063363a4609e0fb3ec9cdc9138c36742537ecdc51786","abstract_canon_sha256":"babc1a129936dba162a28267f68c10dc36473e7b3056eec94e4000c7920a288c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:56:11.552850Z","signature_b64":"Mjti7xZ8BB2Yl8fPYafpHMQzNcKVl29mwX7Tr/EVfcfSof0+9et1SE0sXJoEuSi9LFh5DSkm0sRDkIeVtNUYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff0585b4ccd8c50db8320de47a9e417c22d6bfc9030f9a05162a61bb3801ae87","last_reissued_at":"2026-07-05T03:56:11.552385Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:56:11.552385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics near Couette flow for the $\\beta$-plane equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Hao Zhu, Luqi Wang, Zhifei Zhang","submitted_at":"2022-02-11T15:43:04Z","abstract_excerpt":"In this paper, we study stationary structures near the planar Couette flow in Sobolev spaces on a channel $\\mathbb{T}\\times[-1,1]$, and asymptotic behavior of Couette flow in Gevrey spaces on $\\mathbb{T}\\times\\mathbb{R}$ for the $\\beta$-plane equation. Let $T>0$ be the horizontal period of the channel and $\\alpha={2\\pi\\over T}$ be the wave number. 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