|In this talk we will consider different Navier-Stokes equations modified by the presence of a damping term.
We show in what conditions the solutions of the associated initial and boundary-value problem extinct in a finite time and we study the large time behavior of the solutions as well.
We also shall consider the case when anisotropy is present whether in the diffusion or in the damping term.
This talk is based, in part, in the following references:
 S.N. Antontsev and H.B. de Oliveira, Asymptotic behavior of trembling fluids, To appear in Nolinear Analysis: Real World Applications (2014).
 H.B. de Oliveira, Existence of weak solutions for the generalized Navier-Stokes equations with damping. NoDEA Nonlinear Differential Equations Appl. 20 (2013) no. 3, 797-824.