Existence theory for generalized Newtonian fluids

The flow of a homogeneous generalized Newtonian fluid is described by a generalized Navier-Stokes system whit a shear rate dependent viscocity. In the common power law model the stress deviator is given by S(epsilon(v)) = (1 + vertical bar epsilon(v)vertical bar)(p-2)epsilon(v) with p is an element of (1, infinity). In this note we give an overview about results concerning the existence of weak solutions to these equations in the stationary and non-stationary setting. We present the different techniques which are based on monotone operator theory, L-infinity-truncation and Lipschitz truncation respectively.