Green functions for pressure of Stokes systems

We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\mathrm{\Omega }\subset {\mathbb{R}}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions, and $\mathrm{\Omega }$ is such that the divergence equation is solvable there. We also establish global pointwise bounds for the Green function and its derivatives when coefficients have Dini mean oscillation and $\mathrm{\Omega }$ has a $C^{1,\mathrm{D}\mathrm{i}\mathrm{n}\mathrm{i}}$ boundary. Green functions for the flow velocity of Stokes systems are also considered.