  This paper investigates the global well-posedness and large-time behavior of
solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the
isothermal compressible Euler-Poisson system and incompressible Navier-Stokes
equations coupled through the drag force. Notably, we exploit the dissipation
effects inherent in the Poisson equation to achieve a faster decay of fluid
density compared to velocities. This strategic utilization of dissipation,
together with the influence of the electric field and the damping structure
induced by the drag force, leads to a remarkable decay behavior: the fluid
density converges to equilibrium at a rate of $(1+t)^{-11/4}$, significantly
faster than the decay rates of velocity differences $(1+t)^{-7/4}$ and
velocities themselves $(1+t)^{-3/4}$ in the $L^2$ norm. Furthermore, under the
condition of vanishing coupled incompressible flow, we demonstrate an
exponential decay to a constant state for the solution of the corresponding
system, the damped Euler-Poisson system.
