Initial layer of the incompressible Oldroyd-B model for weakly viscoelastic fluids at the low Weissenberg number

Abstract

This paper is concerned with the Newtonian limit of the incompressible Oldroyd-B model for weakly viscoelastic fluids when the Weissenberg number tends to zero. The convergence rates and the thickness of initial layer are obtained. An effective dynamics is constructed to capture the behavior of initial layer via the method of asymptotic expansions.