  In this paper, we investigate the fluid/gravity correspondence in spacetime
with general non-rotating weakly isolated horizon. With the help of Petrov-like
boundary condition and large mean curvature limit, we show that the dual
hydrodynamical system is described by a generalized forced incompressible
Navier-Stocks equation. Specially, for stationary black holes or those
spacetime with some asymptotically stationary conditions, such a system reduces
to a standard forced Navier-Stocks system.
