Partial Regularity of Suitable Weak Solutions to the System of the Incompressible Non-Newtonian Fluids

AbstractIn this paper, we investigate the partial regularity of the generalized solutions (which are called the suitable weak solutions) to the modified Navier–Stokes equations which describes the dynamics of the incompressible monopolar non-Newtonian fluids. It is proved that the singular points are concentrated on a closed set whose 5−2p (for p⩽52) dimensional Hausdorff measure is zero, and the solution is a regular one (for p>52)