  Using fluid/gravity correspondence, we determine the (linearized) stress
energy tensor of $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling
with all orders in derivatives of fluid velocity included. We find that the
dissipative effects are fully encoded in the shear term and a new one, which
emerges starting from the third order. We derive, for the first time, closed
linear holographic RG flow-type equations for (generalized) momenta-dependent
viscosity functions. In the hydrodynamic regime, we obtain the stress tensor up
to third order in derivative expansion analytically. We then numerically
determine the viscosity functions up to large momenta. As a check of our
results, we also derive the generalized Navier-Stokes equations from the
Einstein equations in the dual gravity.
