It is important to note that although the shock wave in the flyer is relativistic, i.e. us2 w c, the shock wave in the target is not relativistic, namely us2 is smaller than 0.05c for a flyer velocity up to 0.9c. However, the relativistic formalism is important even for the target since in this case we get a target compression of 4 for finite pressures, of the order of 1012 bars, while in the non-relativistic formalism when using the ideal gas EOS (like in our case above) one needs an infinite pressure for a compression of 4.