We have to apply different math for fluids that don't satisfy the viscosity equation. I haven't dug too much into it though...
From it's definition the equation that we use for viscosity isn't a fundamental law, but something like Hooke's law or Ohm's law, which only relates physical quantities with each other. Think of it as an approximation. If we don't need to much accuracy in our measurements and calculations it's "good enough".
RE: Physics - Classical Mechanics - Viscosity and Turbulence