The energy equality for weak solutions to the equations of non-Newtonian fluids

In this short paper, we extend the result of Shinbrot (1974) to an incompressible fluid with shear dependent viscosity. It is shown that a weak solution to the equations of non-Newtonian fluids lying in a space Lq(0,T;Lp) satisfies an energy equality, where 2rr−1≤p≤2rr−2 and 1p+1q≤r−1r, if r>2; p≥2rr−1 and r−1p+1q=r−12, if 2(n+1)n+2