{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:54:41Z","timestamp":1760057681419,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Isle of Man government","award":["unknown"],"award-info":[{"award-number":["unknown"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The pairing of non-relativistic and relativistic Lagrangians within the context of fluid mechanics, advancing methodologies for constructing Poincare-invariant Lagrangians, is explored. Through leveraging symmetries and Noether\u2019s theorem in an inverse framework, three primary cases are investigated: potential flow, barotropic flow expressed in terms of Clebsch variables, and an extended Clebsch Lagrangian incorporating thermodynamic effects. To ensure physical correctness, the eigenvalue relation of the energy\u2013momentum tensor, together with velocity normalisation, are applied as key criteria. The findings confirm that the relativistic Lagrangians successfully reduce to their non-relativistic counterparts in the limit c\u2192\u221e. These results demonstrate a systematic approach that enhances the relationship between symmetries and variational formulations, providing the advantage of deriving Lagrangians that unify non-relativistic and relativistic theories.<\/jats:p>","DOI":"10.3390\/sym17030315","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T04:03:17Z","timestamp":1740024197000},"page":"315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-Relativistic and Relativistic Lagrangian Pairing in Fluid Mechanics Inspired by Quantum Theory"],"prefix":"10.3390","volume":"17","author":[{"given":"Sara","family":"Ismail-Sutton","sequence":"first","affiliation":[{"name":"Department of Engineering, Durham University, Durham DH1 3LE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6945-5247","authenticated-orcid":false,"given":"Markus","family":"Scholle","sequence":"additional","affiliation":[{"name":"Institute for Flow in Additively Manufactured Porous Media (ISAPS), Heilbronn University, Max-Planck-Stra\u00dfe 39, D-74081 Heilbronn, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8572-8997","authenticated-orcid":false,"given":"Philip H.","family":"Gaskell","sequence":"additional","affiliation":[{"name":"Department of Engineering, Durham University, Durham DH1 3LE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","unstructured":"Goldstein, H., Pool, C., and Safko, J. 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