A note on the steady Poiseuille flow of Carreau-Yasuda fluid

The steady Poiseuille flow of Carreau-Yasuda fluid in a pipe, caused by constant pressure gradient, is studied theoretically. It is proved that at some values of the viscosity model parameters, the problem has a classical solution, while at others - generalized solution. For the latter, a necessary and sufficient condition is found, which depends on the pressure gradient and Carreau-Yasuda model parameters.