  We present an analytical study of a toy model for shear banding, without
normal stresses, which uses a piecewise linear approximation to the flow curve
(shear stress as a function of shear rate). This model exhibits multiple
stationary states, one of which is linearly stable against general
two-dimensional perturbations. This is in contrast to analogous results for the
Johnson-Segalman model, which includes normal stresses, and which has been
reported to be linearly unstable for general two-dimensional perturbations.
This strongly suggests that the linear instabilities found in the
Johnson-Segalman can be attributed to normal stress effects.
