  We study a modified three-dimensional incompressible anisotropic
Navier-Stokes equations. The modification consists in the addition of a power
term to the nonlinear convective one. This modification appears naturally in
porous media when a fluid obeys the Darcy-Forchheimer law instead of the
classical Darcy law. We prove global in time existence and uniqueness of
solutions without assuming the smallness condition on the initial data. This
improves the result obtained for the classical 3D incompressible anisotropic
Navier-Stokes equations.
