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We prove the existence of regular dissipative solutions and global attractorsfor the 3D Brinkmann-Forchheimer equations with the nonlinearity of anarbitrary polynomial growth rate. In order to obtain this result, we prove themaximal regularity estimate for the corresponding semi-linear stationary Stokesproblem using some modification of the nonlinear localization technique. Theapplications of our results to the Brinkmann-Forchheimer equation with theNavier-Stokes inertial term are also considered.

Smooth Attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities