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Nguyen","submitted_at":"2023-09-25T08:02:57Z","abstract_excerpt":"We construct finite time blowup solutions to the parabolic-elliptic Keller-Segel system\n  $\\partial_t u = \\Delta u - \\nabla \\cdot (u \\nabla \\mathcal{K}_u), \\quad -\\Delta \\mathcal{K}_u = u \\quad \\textup{in}\\;\\; \\mathbb{R}^d,\\; d = 3,4,$\n  and derive the final blowup profile\n  $ u(r,T) \\sim c_d \\frac{|\\log r|^\\frac{d-2}{d}}{r^2} \\quad \\textup{as}\\;\\; r \\to 0, \\;\\; c_d > 0.$\n  To our knowledge this provides a new blowup solution for the Keller-Segel system, rigorously answering a question by Brenner, Constantin, Kadanoff, Schenkel, and Venkataramani (Nonlinearity, 1999)."},"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":"2309.13932","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2023-09-25T08:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"422d76318669bbb35c6ed34e7ff7ec316fa360caa9c8933429467426ecb18db4","abstract_canon_sha256":"ada69ef2c6e85e2fdb70d0bd5bd4e185f042f75397e5319da4fe41393ec1778d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:06.675768Z","signature_b64":"qSFQrxycSafIzV0dWTQd+AG8VBQRzqtX9DUdEYJJVVRgNOCxvziyV9AV0QzlrNJx77HO099CvkJT1aH1LpqPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c7707b6a0ae8f3a4489c50608a4cd5fd7cf2ca920ec164fd2a9cdc33ca8b997","last_reissued_at":"2026-07-05T09:55:06.675298Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:06.675298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"H. 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