Existence Theory for Generalized Newtonian Fluids

Chapter 3

Solenoidal Lipschitz truncation

Abstract

In this chapter we present the solenoidal Lipschitz truncation for stationary problems: we show how to construct a Lipschitz truncation which preserves the divergence-free character of a given Sobolev function. In the two-dimensional case we improve the method so that function spaces can be included which are not uniformly convex. This is of crucial importance for the Prandtl–Eyring fluid model. Finally, we present the $\mathcal{A}$-Stokes approximation for stationary problems. It aims at approximating almost solutions to the linear $\mathcal{A}$-Stokes system by exact solutions. Thanks to the solenoidal Lipschitz ...