We numerically solve the time-dependent planar Poiseuille flow of a Johnson–Segalman
fluid with added Newtonian viscosity. We consider the case where the shear stress/shear
rate curve exhibits a maximum and a minimum at steady state. Beyond a critical volumetric
flow rate, there exist infinite piecewise smooth solutions, in addition to the standard smooth
one for the velocity. The corresponding stress components are characterized by jump
discontinuities, the number of which may be more than one. Beyond a second critical …