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Two frameworks are considered, regarding in particular the initial position density: Gaussian initial density, or smooth initial density away from vacuum. For Gaussian initial densities, the analysis also yields global solutions to the isothermal Euler system that do not enter the frame of regular solutions to hyperbolic systems by P.D.\u00a0Lax.<\/jats:p>","DOI":"10.3233\/asy-171412","type":"journal-article","created":{"date-parts":[[2017,3,17]],"date-time":"2017-03-17T10:43:58Z","timestamp":1489747438000},"page":"99-117","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective"],"prefix":"10.1177","volume":"102","author":[{"given":"R\u00e9mi","family":"Carles","sequence":"first","affiliation":[{"name":"CNRS, Institut Montpelli\u00e9rain Alexander Grothendieck, UMR 5149, University Montpellier, CC51, 34095 Montpellier, France. 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