  We consider the viscous incompressible fluids in a three-dimensional
horizontally periodic domain bounded below by a fixed smooth boundary and above
by a free moving surface. The fluid dynamics are governed by the Navier-Stokes
equations with the effect of gravity and surface tension on the free surface.
We develop a global well-posedness theory by a nonlinear energy method in low
regular Sobolev spaces with several techniques, including: the horizontal
energy-dissipation estimates, a new tripled bootstrap argument inspired by Guo
and Tice [Arch. Ration. Mech. Anal.(2018)]. Moreover, the solution decays
asymptotically to the equilibrium in an exponential rate.
