  In this paper, we consider the Cauchy problem for an inviscid compressible
Oldroyd-B model in three dimensions. The global well posedness of strong
solutions and the associated time-decay estimates in Sobolev spaces are
established near an equilibrium state. The vanishing of viscosity is the main
challenge compared with our previous work [47] where the viscosity coefficients
are included and the decay rates for the highest-order derivatives of the
solutions seem not optimal. One of the main objectives of this paper is to
develop some new dissipative estimates such that the smallness of the initial
data and decay rates are independent of the viscosity. In addition, it proves
that the decay rates for the highest-order derivatives of the solutions are
optimal. Our proof relies on Fourier theory and delicate energy method. This
work can be viewed as an extension of [47].
