Abstract
This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. We provide a detailed description of the effect of the singular pressure on the breakdown of the smooth solutions. Moreover, we rigorously justify the singular limit for smooth solutions towards the free-congested Euler equations, where the compressible (free) dynamics is coupled with the incompressible one in the constrained (i.e. congested) domain.
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