  We prove the existence of regular dissipative solutions and global attractors
for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an
arbitrary polynomial growth rate. In order to obtain this result, we prove the
maximal regularity estimate for the corresponding semi-linear stationary Stokes
problem using some modification of the nonlinear localization technique. The
applications of our results to the Brinkmann-Forchheimer equation with the
Navier-Stokes inertial term are also considered.
