English

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

Analysis of PDEs 2011-01-24 v1

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.

Keywords

Cite

@article{arxiv.1101.4070,
  title  = {Smooth Attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities},
  author = {Varga K. Kalantarov and Sergey Zelik},
  journal= {arXiv preprint arXiv:1101.4070},
  year   = {2011}
}