Partial Regularity of Suitable Weak Solutions to the System of the Incompressible Shear-thinning Flow

This paper is devoted to the partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow in a bounded domain Ω ⊂ ℝn, n ≥ 2. It is proved that there exists a suitable weak solution of the shear-thinning fluid in the n-D smooth bounded domain (for n ≥ 2). For 3D model, it is proved that the singular points are concentrated on a closed set whose 1 dimensional Hausdorff measure is zero.