On Regularity of Incompressible Fluid with Shear Dependent Viscosity

The authors consider a non-Newtonian fluid governed by equations with p-structure in a cubic domain. A fluid is said to be shear thinning (or pseudo-plastic) if 1 < p < 2, and shear thickening (or dilatant) if p > 2. The case p > 2 is considered in this paper. To improve the regularity results obtained by Crispo, it is shown that the secondorder derivatives of the velocity and the first-order derivative of the pressure belong to suitable spaces, by appealing to anisotropic Sobolev embeddings.