Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay. (English) Zbl 1471.35236
Summary: This paper is concerned with the pullback dynamics and asymptotic stability for a 3D Brinkman-Forchheimer equation with infinite delay. The well-posedness of weak solution to the 3D Brinkman-Forchheimer flow with infinite delay is investigated in the weighted space \(C_\kappa(H)\) firstly, then the pullback attractors are presented for the process of weak solution. Moreover, the existence of global attractor and the exponential stability analysis of stationary solutions are shown, which is based on the estimate of corresponding steady state equation.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B41 | Attractors |
| 35B35 | Stability in context of PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35R07 | PDEs on time scales |
Keywords:
Brinkman-Forchheimer equation; infinite delay; pullback attractors; stationary solution; stabilityReferences:
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