In this talk we shall give a physical motivation for the study of Navier-Stokes type problems modified in the momentum equation by the presence of a damping term. This term is introduced in the equations, by considering a feedback forces field, i.e. a body forces depending not only on the space and time variables, but also on the own velocity. The most significant point, from the physical point of view, is that the consideration of a sublinear damping term leads to the extinction of the fluid in a finite time or its confinement in a certain subdomain. These properties goes beyond the known results for the solutions of classical Navier-Stokes type problems for which we mainly can prove some decays to zero. We shall discuss also existence and uniqueness results for these problems. Finally we shall give some possible applications such as the influence of the Coriolis force in stopping a geostrophic flow or the important problem of confining a hot plasma in some nuclear fusion devices.