Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Chiodaroli, ElisabettaKreml, Ondrej2018-12-132018-12-132018-12-132018-04-0110.1088/1361-6544/aaa10dhttps://infoscience.epfl.ch/handle/20.500.14299/152314WOS:000426927400002We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch. Ration. Mech. Anal. 195 225-60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019-49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.Mathematics, AppliedPhysics, MathematicalMathematicsPhysicsriemann problemnon-uniquenessweak solutionsconvex integrationcompressible euler equationshyperbolic conservation-lawsrarefaction waveswell-posednesssystemuniquenessstabilitydissipationdynamicsgasNon-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equationstext::journal::journal article::research article