Stabilization of Kelvin-Voigt viscoelastic Fuid Fow model
For mathematicians studying viscoelastic fluid dynamics, this provides a theoretical convergence result, but it is incremental as it extends known techniques to a specific model.
The paper proves stabilization (convergence of unsteady to steady solution) for the Kelvin-Voigt viscoelastic fluid flow model, showing power and exponential convergence under certain conditions, with results uniform in the regularization parameter as it approaches zero, thereby extending to the Navier-Stokes system.
In this article, stabilization result for the viscoelastic fluid flow problem 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 $κ$ as $κ\to 0$, which in turn, establishes results for the Navier-Stokes system.