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

作者：Chiodaroli Elisabetta; Kreml Ondrej^*

来源：Nonlinearity, 2018, 31(4): 1441-1460.

DOI：10.1088/1361-6544/aaa10d

• Riemann problem
• non-uniqueness
• weak solutions
• convex integration
• compressible Euler equations

We 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.

• 出版日期2018-4