chapter  12
9 Pages

On Existence Results for Fluids with Shear Dependent Viscosity - Unsteady Flows

ByJ. Frehse, J. Málek, M. Steinhauer

New existence results for the system describing unsteady motion of incompressible fluids with shear dependent viscosity are presented. The nonlinear elliptic operator, which is related to the stress tensor, satisfies the p coercivity condition and is strictly monotone. We prove global existence of weak solutions if p > 2 ( d + 1 ) d + 2 for the space periodic problem; and for no-stick boundary conditions.