A convex integration solution with lower action than the 1-D Riemann solution is constructed, so the least action admissibility principle fails to select the physically intuitive solution.
The Euler equations as a differential inclusion
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Failure of the least action admissibility principle in the context of the compressible Euler equations
A convex integration solution with lower action than the 1-D Riemann solution is constructed, so the least action admissibility principle fails to select the physically intuitive solution.