On the convergence of viscoelastic fluid flows to a steady state

Abstract

The initial-boundary value problems describing motion of a two-dimensional viscoelastic fluid are investigated by using the methods of variational formulation and inequality estimates. Both the exponential and power convergence of the solutions to a steady state solution of the viscoelastic fluid flows are proved under prescribed conditions. The convergences to a stead state solution of the Navier-Stokes flows is a special case of the results.