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

Varga K. Kalantarov; Sergey Zelik

doi:10.3934/cpaa.2012.11.2037

Article Contents

2012, Volume 11, Issue 5: 2037-2054. Doi: 10.3934/cpaa.2012.11.2037

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

Varga K. Kalantarov^1, and
Sergey Zelik^2,

1.
Department of Mathematics, Koç University, Istanbul
2.
Department of Mathematics, University of Surrey, Guildford, GU2 7XH

Received: May 2011

Revised: December 2011

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 35Q35.

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