  We use the AdS/CFT correspondence to argue that large rotating black holes in
global AdS(D) spaces are dual to stationary solutions of the relativistic
Navier-Stokes equations on S**(D-2). Reading off the equation of state of this
fluid from the thermodynamics of non-rotating black holes, we proceed to
construct the nonlinear spinning solutions of fluid mechanics that are dual to
rotating black holes. In all known examples, the thermodynamics and the local
stress tensor of our solutions are in precise agreement with the thermodynamics
and boundary stress tensor of the spinning black holes. Our fluid dynamical
description applies to large non-extremal black holes as well as a class of
large non-supersymmetric extremal black holes, but is never valid for
supersymmetric black holes. Our results yield predictions for the
thermodynamics of all large black holes in all theories of gravity on AdS
spaces, for example, string theory on AdS(5) x S**5 and M theory on AdS(4) x
S**7 and AdS(7) x S**4.
