{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T14:19:01Z","timestamp":1772374741396,"version":"3.50.1"},"reference-count":6,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T00:00:00Z","timestamp":1611532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["18-29-10013"],"award-info":[{"award-number":["18-29-10013"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Quotients of partial differential equations are discussed. The quotient equation for the Euler system describing a one-dimensional gas flow on a space curve is found. An example of using the quotient to solve the Euler system is given. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations (ODEs). Possible solutions of the ODE system are discussed.<\/jats:p>","DOI":"10.3390\/sym13020186","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:28:31Z","timestamp":1611577711000},"page":"186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Quotients of Euler Equations on Space Curves"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8162-045X","authenticated-orcid":false,"given":"Anna","family":"Duyunova","sequence":"first","affiliation":[{"name":"V. A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya Street, 65, 117997 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6000-5063","authenticated-orcid":false,"given":"Valentin","family":"Lychagin","sequence":"additional","affiliation":[{"name":"V. A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya Street, 65, 117997 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1980-6114","authenticated-orcid":false,"given":"Sergey","family":"Tychkov","sequence":"additional","affiliation":[{"name":"V. A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya Street, 65, 117997 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2435","DOI":"10.1134\/S1995080220120100","article-title":"Symmetries and differential invariants for inviscid flows on a curve","volume":"41","author":"Duyunova","year":"2020","journal-title":"Lobachevskii J. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1134\/S1995080220030129","article-title":"Critical Phenomena in Filtration Processes of Real Gases","volume":"41","author":"Lychagin","year":"2020","journal-title":"Lobachevskii J. Math."},{"key":"ref_3","unstructured":"Krasilchchik, I., Vinogradov, A.M., and Lychagin, V.V. (1986). Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach Science Publishers."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"401","DOI":"10.2307\/2372523","article-title":"Some basic theorems on algebraic groups","volume":"78","author":"Rosenlicht","year":"1956","journal-title":"Am. J. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02418270","article-title":"Sur les invariants diff\u00e9rentiels des groupes continus de transformations","volume":"18","author":"Tresse","year":"1894","journal-title":"Acta Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1007\/s00029-015-0220-z","article-title":"Global Lie\u2013Tresse theorem","volume":"22","author":"Kruglikov","year":"2016","journal-title":"Sel. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/186\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:14:52Z","timestamp":1760159692000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,25]]},"references-count":6,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020186"],"URL":"https:\/\/doi.org\/10.3390\/sym13020186","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,25]]}}}