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

By Varga K. Kalantarov, Sergey Zelik. 2011

119 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df8e482d32900ba3d8249b9d287f46c2dc34fb56

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Energy equality for the 3D critical convective Brinkman–Forchheimer equations (2016, background): “For larger values of the exponent r > 3, it was already shown that the CBF equations enjoy existence of global-in-time strong solutions (see proof for bounded domains in [7]) and hence the energy equality is satisfied.”
Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces (2019, background): “Unlike the Navier–Stokes equations themselves, for which known results are a long way from providing the global existence of regular solutions, for the CBF equations strong solutions u ∈ L(0, T ;H(1) 0 ) ∩ L (2)(0, T ;H(2)) are known to exist for all time for every r > 2 (Kalantarov & Zelik [16]; se”
Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model (2015, background): “This result was already obtained in [3, 17].”