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We consider the limit when the thickness tends to zero and we prove that the three characteristic regimes for Newtonian fluids are still valid for non-Newtonian fluids, i.e. Stokes roughness ($\\eta_\\varepsilon\\approx \\varepsilon$), Reynolds roughness ($\\eta_\\varepsilo"},"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":"1712.06005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-16T18:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"8df02504952c472426ae5d5cb339380790119fbc6a04b740c401a53b5eb87607","abstract_canon_sha256":"25a9d5ab121b6d199d3dbc04fc6c4bec2203bdc9bcfa633fa26f009cce8d64ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:51.315989Z","signature_b64":"Sl2kdpDR7Y278M6W+gI0uJXHDSA543MmJAKfHbRpMgyyzTlav3QrUNa5wAt9dtI51iGm5el1YSbM83zF6HxoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38facd9ac7a347cc187a553279db493199912811de542d45cf6d970cb9b42a73","last_reissued_at":"2026-05-18T00:27:51.315535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:51.315535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francisco J. 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