  In Stokes flow, the stream function associated with the velocity of the fluid
satisfies the biharmonic equation. The detailed behavior of solutions to the
biharmonic equation on regions with corners has been historically difficult to
characterize. The problem was first examined by Lord Rayleigh in 1920; in 1973,
the existence of infinite oscillations in the domain Green's function was
proven in the case of the right angle by S.~Osher. In this paper, we observe
that, when the biharmonic equation is formulated as a boundary integral
equation, the solutions are representable by rapidly convergent series of the
form $\sum_{j} ( c_{j} t^{\mu_{j}} \sin{(\beta_{j} \log{(t)})} + d_{j}
t^{\mu_{j}} \cos{(\beta_{j} \log{(t)})} )$, where $t$ is the distance from the
corner and the parameters $\mu_{j},\beta_{j}$ are real, and are determined via
an explicit formula depending on the angle at the corner. In addition to being
analytically perspicuous, these representations lend themselves to the
construction of highly accurate and efficient numerical discretizations,
significantly reducing the number of degrees of freedom required for the
solution of the corresponding integral equations. The results are illustrated
by several numerical examples.
