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Pullback attractors for a two-dimensional Navier-Stokes model in an infinite delay case. (English) Zbl 1218.35045

The existence of solutions for a Navier-Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space \(C_\gamma(H)\) is proved. Then, under additional suitable assumptions, the authors prove the existence and uniqueness of a stationary solution and the exponential decay of the solutions of the evolutionary problem to this stationary solution. The existence of pullback attractors for the dynamical system associated to the problem is proved under more general assumptions.

MSC:

35B41 Attractors
35K55 Nonlinear parabolic equations
35Q30 Navier-Stokes equations
34D45 Attractors of solutions to ordinary differential equations
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