Geometric Constraints for Global Regularity of 3D Shear Thickening Fluids

We consider the relation between the direction of the vorticity and the global regularity of 3D shear thickening fluids. It is showed that a weak solution to the non-Newtonian incompressible fluid in the whole space is strong if the direction of the vorticity is \({{11 - 5p} \over 2}\) $$\frac{11-5p}{2}$$ -Hölder continuous with respect to the space variables when \(2 < p < {{11} \over 5}\) $$2<p<\frac{11}{5}$$ .