{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:15:37Z","timestamp":1777454137333,"version":"3.51.4"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T00:00:00Z","timestamp":1571961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["HA 6471\/2-1"],"award-info":[{"award-number":["HA 6471\/2-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Liquid\u2013vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575\u2013591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.<\/jats:p>","DOI":"10.3390\/e21111039","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T11:05:18Z","timestamp":1572001518000},"page":"1039","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations"],"prefix":"10.3390","volume":"21","author":[{"given":"Maren","family":"Hantke","sequence":"first","affiliation":[{"name":"Institute for Mathematics, Martin-Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0170-8284","authenticated-orcid":false,"given":"Ferdinand","family":"Thein","sequence":"additional","affiliation":[{"name":"Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, PSF 4120, D-39016 Magdeburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S1874-5792(02)80011-8","article-title":"Dynamic flows with liquid\/vapor phase transitions","volume":"Volume 1","author":"Friedlander","year":"2002","journal-title":"Handbook of Mathematical Fluiddynamics"},{"key":"ref_2","unstructured":"Zein, A. (2010). Numerical Methods for Multiphase Mixture Conservation Laws with Phase Transition. [Ph.D. Thesis, Otto-von-Guericke-Universit\u00e4t Magdeburg]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF00375400","article-title":"Kinetic relations and the propagation of phase boundaries in solids","volume":"114","author":"Abeyaratne","year":"1991","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_4","unstructured":"Hantke, M., and Thein, F. (2017). A general existence result for isothermal two-phase flows with phase transition. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1090\/S0033-569X-2013-01290-X","article-title":"Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition","volume":"71","author":"Hantke","year":"2013","journal-title":"Q. Appl. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1090\/qam\/1393","article-title":"Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations","volume":"73","author":"Hantke","year":"2015","journal-title":"Quart. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1874-5717(06)80004-6","article-title":"Euler Equations and Related Hyperbolic Conservation Laws","volume":"Volume 2","author":"Dafermos","year":"2005","journal-title":"Handbook of Differential Equations Evolutionary Equations"},{"key":"ref_8","unstructured":"Thein, F. (2018). Results for Two Phase Flows with Phase Transition. [Ph.D. Thesis, Otto-von-Guericke-Universit\u00e4t Magdeburg]."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Dafermos, C.M. (2000). Hyperbolic Conservation Laws in Continuum Physics, Springer.","DOI":"10.1007\/978-3-662-22019-1"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"LeFloch, P. (2002). Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Lectures in Mathematics, Birkh\u00e4user Verlag.","DOI":"10.1115\/1.1579455"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bartelmann, M., Feuerbacher, B., Kr\u00fcger, T., L\u00fcst, D., Rebhan, A., and Wipf, A. (2015). Theoretische Physik, Springer Spektrum.","DOI":"10.1007\/978-3-642-54618-1"},{"key":"ref_12","unstructured":"Landau, L.D., and Lifschitz, E.M. (1987). Lehrbuch der theoretischen Physik, Bd. V Statistische Physik, Akad.-Verl.. [8th ed.]."},{"key":"ref_13","unstructured":"Wagner, W., and Kruse, A. (1998). Properties of Water and Steam: The Industrial Standard IAPWS-IF97 for the Thermodynamic Properties and Supplementary Equations for Other Properties: Tables Based on These Equations, Springer."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1007\/s00574-016-0185-3","article-title":"Singular and selfsimilar solutions for Euler equations with phase transitions","volume":"47","author":"Hantke","year":"2016","journal-title":"Bull. Braz. Math. Soc. (N.S.)"},{"key":"ref_15","unstructured":"M\u00fcller, I. (1985). Thermodynamics, Pitman."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/s00161-011-0225-6","article-title":"Bubbles in liquids with phase transition. Part 1. On phase change of a single vapor bubble in liquid water","volume":"24","author":"Dreyer","year":"2012","journal-title":"Contin. Mech. Thermodyn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1039\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:29:27Z","timestamp":1760189367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1039"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,25]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["e21111039"],"URL":"https:\/\/doi.org\/10.3390\/e21111039","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,25]]}}}