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

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Zelik, Sergey

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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.

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Amer Inst Mathematical Sciences

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Mathematics, Applied mathematics

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Communications On Pure and Applied Analysis

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10.3934/cpaa.2012.11.2037

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