Soft congestion approximation to the one-dimensional constrained Euler equations

This article is concerned with the analysis of one-dimensional compressible Euler equations a singular pressure law, so-called hard sphere equation state. The result twofold. First, we establish existence bounded weak solutions by means viscous regularization and refined compensated compactness arguments. Second, investigate smooth setting providing detailed description impact on breakdown solutions. In this framework, rigorously justify limit towards free-congested equations, where (free) dynamics coupled incompressible one in constrained (i.e. congested) domain.