  In this work we consider the generalized Navier-Stoke equations with the
presence of a damping term in the momentum equation. % The problem studied here
derives from the set of equations which govern the isothermal flow of
incompressible, homogeneous and non-Newtonian fluids. % For the generalized
Navier-Stokes problem with damping, we prove the existence of weak solutions by
using regularization techniques, the theory of monotone operators and
compactness arguments together with the local decomposition of the pressure and
the Lipschitz-truncation method. The existence result proved here holds for any
$q>\frac{2N}{N+2}$ and any $\sigma>1$, where $q$ is the exponent of the
diffusion term and $\sigma$ is the exponent which characterizes the damping
term.
