  We consider global-in-time evolution of irrotational, isentropic,
compressible Euler flow in $3$-D, for a broad class of $H^4$ classical Cauchy
data without assuming symmetry, prescribed on an annulus surrounded by a
constant state in the exterior. By giving a sufficient condition on the initial
data and using the nonlinear structure of the compressible Euler equations, we
show that the decay rate of the first order transversal derivative of the
normalized density is better than that of the same derivative of a free wave,
provided that the perturbation arising from the tangential derivatives can be
properly controlled for all $t$ by using a bootstrap argument. Based on this
key analysis, we construct global exterior solutions in $H^4$ for the broad
class of data, with a rather general subclass forming rarefaction at null
infinity. Our result does not require smallness on the transversal derivatives
of classical data, thus applies to data with a total energy of any size.
