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We consider the one-dimensional Cauchy problem for the Navier-Stokes equations with degenerate viscosity coefficient in highly compressible regime. It corresponds to the compressible Navier-Stokes system with large Mach number equal to ε −1/2 for ε going to 0. When the initial velocity is related to the gradient of the initial density, the densities solving the compressible Navier-Stokes equations -ρε converge to the unique solution to the porous medium equation [14, 13] . For viscositydoi:10.3934/dcds.2016.36.3107 fatcat:kgulekigvvgjdm6zb3cbf42ysu