Existence Theory for Generalized Newtonian Fluids

Appendix B

The $\mathcal{A}$-Stokes system

The aim of this section is to present regularity results for the (non-stationary) $\mathcal{A}$-Stokes system depending on the right hand side (in divergence form). Let us fix for this section a bounded domain $G\subset {\mathbb{R}}^3$ with $C^2$-boundary and a time interval $(0,T)$. Moreover, let $\mathcal{A}:{\mathbb{R}}^{3\times 3}\to {\mathbb{R}}^{3\times 3}$ be an elliptic tensor.

B.1 The stationary problem ...