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The model consists of a single one dimensional evolution equation for the thickness $2h = 2h(x,t)$ of a thin neck of fluid, \\[ \\partial_t h + \\partial_x( h \\, \\partial_x^3 h) = 0\\, , \\] for $x\\in (-1,1)$ and $t\\ge 0$. The boundary conditions fix the neck height and the pressure jump: \\[ h(\\pm 1,t) = 1, \\qquad \\partial_{x}^2 h(\\pm 1,t) = P>0. \\] We prove that starting from smooth and positive $h$, as long as $h(x,t) >0$, for $x\\in "},"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":"1708.08490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-28T19:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"c9addf70254851a386f2adff43c87f14cece50745b39fe7acb5159584bd0d55b","abstract_canon_sha256":"b7682e5a084aecfdcff29a79dceb2ae645216cad82eaed76b42f2bc4cb3fdb1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.429966Z","signature_b64":"e+8XKolL4Fx/KBfJn9OBP519xP3rcGbFyYRnw1yxnf2qIG+opQSGAApuBLNj3JhTPIRbDgtb58OLkziQZdaCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cb9c468b2f1ea9171d94ffdcbe97e7dd330c901e390786bf1224abe083541c2","last_reissued_at":"2026-05-18T00:05:00.429515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.429515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On singularity formation in a Hele-Shaw model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huy Nguyen, Peter Constantin, Tarek Elgindi, Vlad Vicol","submitted_at":"2017-08-28T19:17:33Z","abstract_excerpt":"We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in \\cite{CDGKSZ93} and widely studied since. 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