  The paper presents a solution for axisymmetric propagation of a penny-shaped
crack driven by a thinning fluid. The solution to the accuracy of four
significant digits, at least, is obtained on the basis of the modified
formulation of hydraulic fracture problem by employing the particle velocity,
rather than conventionally used flux. This serves to properly organize
iterations in the opening after reducing the problem to the self-similar form.
Numerical results obtained show relatively small dependence of self-similar
quantities (fracture radius, propagation speed, opening, particle velocity,
pressure, flux) on the behavior index of a thinning fluid. The results provide
bench marks for the accuracy control of truly 3D simulators and they serve for
assigning an apparent viscosity when simulating the action of a thinning fluid
by replacing it with an equivalent Newtonian fluid.
