  Two-dimensional Stokes flow through a periodic channel is considered. The
channel walls need only be Lipschitz continuous, in other words they are
allowed to have corners. Boundary integral methods are an attractive tool for
numerically solving the Stokes equations, as the partial differential equation
can be reformulated into an integral equation that must be solved only over the
boundary of the domain. When the boundary is at least C 1 smooth, the boundary
integral kernel is a compact operator, and traditional Nystr\"om methods can be
used to obtain highly accurate solutions. In the case of Lipschitz continuous
boundaries, however, obtaining accurate solutions using the standard Nystr\"om
method can require high resolution. We adapt a technique known as recursively
compressed inverse preconditioning to accurately solve the Stokes equations
without requiring any more resolution than is needed to resolve the boundary.
Combined with a periodic fast summation method we construct a method that is
O(N log N ) where N is the number of quadrature points on the boundary. We
demonstrate the robustness of this method by extending an existing boundary
integral method for viscous drops to handle the movement of drops near corners.
