So I've got a problem here in fluids. It's driving me insane but I know I'm missing something simple.
Up until now we've worked with Newtonian fluids resulting in the "normal" NS equations in Cartesian coordinates (ie 1). those apply only to non-compressible, Newtonian fluids. We were specifically given the general tensor version of the equations( i.e. ), and some data about the shear stress vs the shear rate, and told it was a power law fluid in this question (so non-Newtonian).
I understand from the derivations for how we get from the "general" NS equation (the screenshot) to the "normal" equation I showed first above, but I cannot figure out how to apply the general form to this power law fluid (which behaves as a pseudoplastic given we have a n < 1). I've searched literature and our textbooks and no one goes through the derivation. Any help?