Boundary value problems for the Stokes and Navier-Stokes systems in polyhedral domains

This is a survey of new results concerning solvability and regularity properties of boundary value problems for the Stokes and Navier-Stokes systems in a three dimensional polyhedral domain. I start with pointwise estimates for Green's tensors of the Stokes operator. Then I turn to estimates of solutions in weighted and nonweighted Sobolev spaces, first for linear and then for nonlinear problems. These results are applied to a free boundary problem for the Navier-Stokes system.