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Thanks to the noise, the solutions that we construct are limits in law of a regularized stochastic Euler equation and enjoy an additional $L^2([0,T];H^{-\\alpha})$ regularity.\n  For every $p>3/2$ and for certain regularity indices $\\alpha \\in (0,1/2)$ of the Kraichnan noise, we show also pathwise uniqueness for every $L^p$ initia"},"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":"2308.03216","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-06T22:03:25Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ae50afc8cdf38f33a526ee91718f911ff8b2e613c055037b6add9f28d7d7a50a","abstract_canon_sha256":"1726274f8c3ba6ccde03288ab73f753ee101fe3a3be596a5f0e32d94f35ad228"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:25.330176Z","signature_b64":"n2CGfqHkutEWTTndb019E6wWEXe0A3DQfL/TtqU8QY51YtJvfb437gWISXCxBJZI8Xlp4GVvr+YqaWyo96suBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c2247e15151ff4e6f0fad75af03fd5fcd49e4188aab3be577a1bf36402df0c5","last_reissued_at":"2026-07-05T08:49:25.329756Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:25.329756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Mario Maurelli, Michele Coghi","submitted_at":"2023-08-06T22:03:25Z","abstract_excerpt":"We consider the 2D Euler equations on $\\R^2$ in vorticity form, with unbounded initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise, with regularity index $\\alpha\\in (0,1)$.\n  We show weak existence for every $\\dot{H}^{-1}$ initial vorticity. 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