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

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  • We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with a nonlinearity of 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.
    Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35Q35.

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