  We study the isentropic Euler equations with time-dependent damping, given by
$\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative
constants to describe the decay rate of damping with respect to time. We will
investigate the global existence and asymptotic behavior of small data
solutions to the Euler equations when $0<\lambda<1,0<\mu$ in multi-dimensions
$n\geq 1$. The asymptotic behavior will coincide with the one that obtained by
many authors in the case $\lambda=0$. We will also show that the solution can
only decay polynomially in time while in the three dimensions, the vorticity
will decay exponentially fast.
