  Small perturbations of a black brane are interpreted as small deviations from
thermodynamic equilibrium in a dual theory with the AdS/CFT correspondence. In
this paper, we calculate hydrodynamics of the dual Yang-Mills theory in the
gravity side using membrane paradigm. This method is different from the usual
AdS/CFT correspondence and evaluate classical solutions not at boundaries but
at the place slightly away from a horizon. There are sound modes or shear modes
for gravity perturbation. For sound modes, such calculation at the horizon has
not yet been done. Then, we find that boundary stress tensor at the horizon
satisfies conservation law in flat space and can represent dissipative parts of
stress tensor in the dual theory by holography. Using them, we can read off
directly shear and bulk viscosity of the dual theory. Quasinormal modes are
solutions to linearized equations obeyed by classical fluctuations of a
gravitational background subject to specific boundary conditions and are also
gauge-invariant quantities. We use solutions for each fluctuation that compose
such quantities and show that quasinormal modes are consistent with the
membrane paradigm.
