Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids

The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data v 0 ∈ J 2 (Ω) and for p ∈ ( 9 5 , 2 ) . It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities.