  In this paper, we present a refined framework for the global-in-time
well-posedness theory for the pressureless Euler--Navier--Stokes system and the
optimal temporal decay rates of certain norms of solutions. Here the coupling
of two systems, pressureless Euler system and incompressible Navier--Stoke
system, is through the drag force. We construct the global-in-time existence
and uniqueness of regular solutions for the pressureless Euler--Navier--Stokes
system without using a priori large time behavior estimates. Moreover, we seek
for the optimal Sobolev regularity for the solutions. Concerning the temporal
decay for solutions, we show that the fluid velocities exhibit the same decay
rate as that of the heat equations. In particular, our result provides that the
temporal decay rate of difference between two velocities, which is faster than
the fluid velocities themselves, are at least the same as the second-order
derivatives of fluid velocities.
