Green functions for pressure of Stokes systems

Abstract

We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain Ω ⊂ R d , where d ≥ 2. We construct the Green function when coefficients are merely measurable in one direction and have Dini mean oscillation in the other directions, and Ω 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 Ω has a C 1,Dini boundary. Green functions for the flow velocity of Stokes systems are also considered.