Spectrally Determined Growth for Creeping Flow of the Upper Convected Maxwell Fluid

Abstract. While it is well known that the stability of Newtonian flows is determined by the eigenvalues of a linearized equation, there are no general results of this type for non-Newtonian fluids. In this paper, we show that linear stability of steady creeping flows of the upper convected Maxwell fluid is indeed determined by the spectrum of the linearized operator. The proof uses the theory of evolution semigroups over dynamical systems.