Stabilization of Kelvin–Voigt viscoelastic fluid flow model

ABSTRACT

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.

KEYWORDS:

• Viscoelastic fluid
• Kelvin–Voigt model
• exponential decay
• power and exponential convergence
• steady state
• stabilization

AMS SUBJECT CLASSIFICATIONS:

• 35B35
• 76D05
• 93D20

Acknowledgements

Both authors thank the referee for his/her valuable suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was financially supported by UGC, Govt. India. The second author was supported by IIT Bombay vide IRCC [project number 13IRAWD007].