Existence Theory for Generalized Newtonian Fluids

Chapter 6

Solenoidal Lipschitz truncation

Abstract

In this chapter we present the solenoidal Lipschitz truncation for non-stationary problems: we show how to construct a Lipschitz truncation which preserves the divergence-free character of a given Sobolev function. As a matter of fact, it suffices to have distributional time-derivatives in the sense of divergence-free test-functions. After this, we present the $\mathcal{A}$-Stokes approximation for non-stationary problems. It aims at approximating almost solutions to the non-stationary $\mathcal{A}$-Stokes system ...