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

2011/01/21 by Varga K. Kalantarov, Kalantarov, Varga K., Sergey Zelik +1 · 2 citations
Mathematics · #35B41 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B41

paper · pdf · doi:10.48550/arxiv.1101.4070

arxiv created 2011/01/21 · arxiv updated 2011/01/24

Abstract

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.

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