On the convergence of viscoelastic fluid flows to a steady state
This paper is concerned with the convergence of unsteady viscoelastic fluid flows to a stady state flow as time goes to infinity. The Oldroyd's mathematical model of incompressible fluids is used to describe the motion of the viscoelastic fluids, leading to generalization of the Navier-Stokes equations. By using the variational approach and various differential inequalities, the authors prove under certain assumptions that solutions to an initial boundary value problem for the unsteady viscoelatic fluid flows converge to a steady state solution exponentially and polynomially as time tends to infinity. As a consequence, the convergence to a steady state solution of the Navier-Stokes flows is a special case of this paper.
scientific article; zbMATH DE number 1983417