Stabilization of Kelvin-Voigt viscoelastic fluid flow model. (English) Zbl 1421.35279
Summary: In this article, stabilization result for the viscoelastic fluid flow problem is governed by Kelvin-Voigt model, that is, convergence of the unsteady solution to a steady state solution is proved under the assumption that linearized self-adjoint steady state eigenvalue problem has a minimal positive eigenvalue. Both power and exponential convergence results are derived under various conditions on the forcing function. It is shown that results are valid uniformly in the time relaxation or some times called regularization parameter \(\kappa\) as \(\kappa\to 0\), which in turn, establishes results for the Navier-Stokes system.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A10 | Viscoelastic fluids |
| 35B35 | Stability in context of PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 93D20 | Asymptotic stability in control theory |
Keywords:
viscoelastic fluid; Kelvin-Voigt model; exponential decay; power and exponential convergence; steady state; stabilizationReferences:
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