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In detail, we obtain a class of global rotational exact solutions for the compressible fluids with $\\gamma>1$:%} [c]{c}% \\rho=\\max\\{\\frac{\\gamma-1}{K\\gamma}[ C^{2}[ x^{2}% +y^{2}+z^{2}-(xy+yz+xz)] -\\dot{a}(t)(x+y+z)+b(t)], 0\\} ^{\\frac{1}{\\gamma-1}} u_{1}=a(t)+C(y-z) u_{2}=a(t)+C(-x+z) u_{3}=a(t)+C(x-y).  where  a(t)=c_{0}+c_{1}t and b(t)=3c_{0}c_{1}t+{3/2}c_{1}^{2}t^{2}+c_{2}% with $C$, $c_{0}$, $c_{1}$ and $c_{2}$ are arbi"},"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":"1105.4216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-21T06:40:59Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"d7137a9bb6047422a90c6f6a98fa203531d5c67d8141d52b39f26166b0ed9ed9","abstract_canon_sha256":"62a777fae0a93e2503aa7085a7504ee518d00de0b9bcca6c0339bdcab08fdbf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:41.958668Z","signature_b64":"T2Iubxmrrrv6oLHdl/ojr05YAhv+tWL/HhaXoiyWu85P/X37pt4Ccz523mZDxM5yMLxhIBTKYZLNQ01nlO+0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16eea32c223f67558af6d0460ac1f201fe6c10b1b86b97eae6e06fd47f2c20cb","last_reissued_at":"2026-05-18T04:16:41.958013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:41.958013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact, Rotational, Infinite Energy, Blowup Solutions to the 3-Dimensional Euler Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Manwai Yuen","submitted_at":"2011-05-21T06:40:59Z","abstract_excerpt":"In this paper, we construct a new class of blowup solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. In detail, we obtain a class of global rotational exact solutions for the compressible fluids with $\\gamma>1$:%} [c]{c}% \\rho=\\max\\{\\frac{\\gamma-1}{K\\gamma}[ C^{2}[ x^{2}% +y^{2}+z^{2}-(xy+yz+xz)] -\\dot{a}(t)(x+y+z)+b(t)], 0\\} ^{\\frac{1}{\\gamma-1}} u_{1}=a(t)+C(y-z) u_{2}=a(t)+C(-x+z) u_{3}=a(t)+C(x-y).  where  a(t)=c_{0}+c_{1}t and b(t)=3c_{0}c_{1}t+{3/2}c_{1}^{2}t^{2}+c_{2}% with $C$, $c_{0}$, $c_{1}$ and $c_{2}$ are arbi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4216","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.4216","created_at":"2026-05-18T04:16:41.958112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4216v1","created_at":"2026-05-18T04:16:41.958112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4216","created_at":"2026-05-18T04:16:41.958112+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3XKGLBCH5TV","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3XKGLBCH5TVLCXW","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3XKGLBC","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH","json":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH.json","graph_json":"https://pith.science/api/pith-number/C3XKGLBCH5TVLCXW2BDAVQPSAH/graph.json","events_json":"https://pith.science/api/pith-number/C3XKGLBCH5TVLCXW2BDAVQPSAH/events.json","paper":"https://pith.science/paper/C3XKGLBC"},"agent_actions":{"view_html":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH","download_json":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH.json","view_paper":"https://pith.science/paper/C3XKGLBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4216&json=true","fetch_graph":"https://pith.science/api/pith-number/C3XKGLBCH5TVLCXW2BDAVQPSAH/graph.json","fetch_events":"https://pith.science/api/pith-number/C3XKGLBCH5TVLCXW2BDAVQPSAH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH/action/storage_attestation","attest_author":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH/action/author_attestation","sign_citation":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH/action/citation_signature","submit_replication":"https://pith.science/pith/C3XKGLBCH5TVLCXW2BDAVQPSAH/action/replication_record"}},"created_at":"2026-05-18T04:16:41.958112+00:00","updated_at":"2026-05-18T04:16:41.958112+00:00"}