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}
}