{"paper":{"title":"Component-wise dimensionally reduced flows and helicity conservation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Jian-Zhou Zhu","submitted_at":"2023-08-17T08:31:46Z","abstract_excerpt":"The component-wise dimensionally reduced real Schur flows (RSFs) associated to the classical compressible Euler equation [J.-Z. Zhu, J. Math. Phys. \\textbf{62}, 083101 (2021)] is reformulated alternatively in terms of mode-truncation, with the untruncated Fourier modes preserving the original interaction structure and thus other important derivatives. A number of results are set up for the mathematical physics of component-wise dimensionally reduced flows (CWDRFs, including those with further dimensional reductions of RSFs); and, it is particularly shown that previous proofs of the helicity in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.11938","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.11938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}