Existence theory for generalized Newtonian fluids

摘要

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(e(v))= (1 + |ε(v)|)~p~(-2)ε(v) with p ε (l,∞). 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~∞-truncation and Lipschitz truncation respectively.