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The pullback-\(\mathcal{D}\) attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer system with delay. (English) Zbl 1410.35101
The authors consider the 3D Kelvin-Voigt-Brinkman-Forchheimer system with continuous delay and prove the existence of pullback-\(\mathcal{D}\) attractors. The method of proof involves establishing the existence of pullback-\(\mathcal{D}\) absorbing sets and the pullback-\(\mathcal{D}\) asymptotic compactness of the associated family of solution processes. The asymptotic compactness result follows the standard decomposition technique for hyperbolic/wave equations treated for non-autonomous source terms (cf. e.g. [V. V. Chepyzhov and M. I. Vishik, Attractors for equations of mathematical physics. Providence, RI: American Mathematical Society (AMS) (2002; Zbl 0986.35001)]).
MSC:
35Q30 Navier-Stokes equations
37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
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