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We use this show that, for sufficiently large $\\beta$, the global attractor of this system reduces to a point."},"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":"1009.4538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-23T08:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"e92127d313b300e96859a2e98932d203692ace363da3ff1c144643614a238439","abstract_canon_sha256":"3d6abb82688c9a240585ee818b2b94169fef1f922fe8a219f90f72c1796e9b68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:30.199232Z","signature_b64":"rycUKBWOd0w5qRplzGOUehsI+e3Qd+RG2mlnobqgbD7nZXfXyo9qkyHFy3wLAqoAw/CVA42x8Dkc9oN1zIIRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c47f1790f6b72f624a2f87ab96365cb343ed87a9d1e3105f3c22cb57a3a44d9","last_reissued_at":"2026-05-18T04:40:30.198563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:30.198563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Navier-Stokes equations on the $\\beta$-plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Djoko Wirosoetisno, Mustafa Al-Jaboori","submitted_at":"2010-09-23T08:13:28Z","abstract_excerpt":"We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier--Stokes equations on the periodic $\\beta$-plane (i.e.\\ with the Coriolis force varying as $f_0+\\beta y$) will become nearly zonal: with the vorticity $\\omega(x,y,t)=\\wb(y,t)+\\wt(x,y,t)$, one has $|\\wt|_{H^s}^2\\le\\beta^{-1} M_s(\\...)$ as $t\\to\\infty$. 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