Chapter 7

# Power law fluids

## Abstract

We study non-stationary motions of power law fluids in a bounded Lipschitz domain. Based on the solenoidal Lipschitz truncation from Chapter 6 we show the existence of weak solutions to the generalized Navier–Stokes system for $p>\frac{2d}{d+2}$. Our approach completely avoids the appearance of the pressure function.

### Keywords

Generalized Newtonian fluids; Power law fluids; Non-stationary flows; Weak solutions; Existence theory; Solenoidal Lipschitz truncation

The flow of a homogeneous incompressible fluid in a bounded body $G\subset {\mathbb{R}}^{d}$ ($d=2,$

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