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Math. Anal."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional nonisentropic Euler equations for compressible fluids. For the isentropic Euler equations, we pinpoint a necessary and sufficient condition for the formation of singularities of solutions with large initial data that allow a far-field vacuum---there exists a compression in the initial data. For the nonisentropic Euler equations, we identify a sufficient condition for the formation of singularities of solutions with large initial data that allow a far-field vacuum---there exists a strong compression in the initial data. Furthermore, we identify two new phenomena---decompression and de-rarefaction---for the nonisentropic Euler flows, different from the isentropic flows, via constructing two respective solutions. For the decompression phenomenon, we construct a first global continuous nonisentropic solution, even though the initial data contain a weak compression, by solving a backward Goursat problem, so that the solution is smooth, except on several characteristic curves across which the solution has a weak discontinuity (i.e., only Lipschitz continuity). For the de-rarefaction phenomenon, we construct a continuous nonisentropic solution whose initial data contain isentropic rarefactions (i.e., without compression) and a locally stationary varying entropy profile, for which the solution still forms a shock wave in a finite time.<\/jats:p>","DOI":"10.1137\/20m1316603","type":"journal-article","created":{"date-parts":[[2021,11,4]],"date-time":"2021-11-04T15:25:52Z","timestamp":1636039552000},"page":"6280-6325","source":"Crossref","is-referenced-by-count":14,"title":["Formation of Singularities and Existence of Global Continuous Solutions for the Compressible Euler Equations"],"prefix":"10.1137","volume":"53","author":[{"given":"Geng","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gui-Qiang G.","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1727","authenticated-orcid":true,"given":"Shengguo","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,11,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219891611002536"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2017.66.5988"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/16M1062818"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2019172"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2011.09.004"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-015-0854-1"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219891613500069"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375416"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02877431"},{"key":"atypb10","volume-title":"CUHK","author":"Chen S.","year":"1999"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.4171\/192"},{"key":"atypb12","volume-title":"Compressible Flow and Euler's Equations","author":"Christodoulou D.","year":"2014"},{"key":"atypb13","volume-title":"Interscience","author":"Courant R.","year":"1948"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-49451-6"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160270307"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-02-02982-3"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1063\/1.1704154"},{"key":"atypb18","first-page":"523","volume":"73","author":"Lebaud M.","year":"1994","journal-title":"J. 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