  We derive globally reliable a posteriori error estimators for a
PDE-constrained optimization problem involving linear models in fluid dynamics
as state equation; control constraints are also considered. The corresponding
local error indicators are locally efficient. The assumptions under which we
perform the analysis are such that they can be satisfied for a wide variety of
stabilized finite element methods as well as for standard finite element
methods. When stabilized methods are considered, no a priori relation between
the stabilization terms for the state and adjoint equations is required. If a
lower bound for the inf-sup constant is available, a posteriori error
estimators that are fully computable and provide guaranteed upper bounds on the
norm of the error can be obtained. We illustrate the theory with numerical
examples.
