Existence of strong solutions to the equations of unsteady motion of shear thickening incompressible fluids. (June 2015) - Bae, Hyeong-Ohk; Wolf, Jörg
Abstract: 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 ( 2 < q < + ∞ ) . In particular, we find that global strong solutions exist whenever 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.