Existence of strong solutions to the equations of unsteady motion of shear thickening incompressible fluids

We address the existence of strong solutions to a system of equations of motion of an incompressible non-Newtonian fluid. Our aim is to prove the short-time existence of strong solutions for the case of shear thickening viscosity, which corresponds to the power law ν(D)=∣D∣q−2(22.23…q>2.23…. The results are obtained by flattening the boundary and by using the difference quotient method. Near the boundary, we use weighted estimates in the normal direction.