Stokes Flow Between Parallel Plates due to a Trausversely Moving End Wall

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Abstract
Consider the two-dimensional Stokes flow in a semi-infinite strip of viscous fluid due to a transverse velocity of its end wall. This is an idealization of the motion in the asthenosphere due to a subducting slab. We give an iterative scheme for calculating the flow, prove existence and uniqueness, and obtain numerical approximations, using developments of Teodorescu's method and an approximate solution of the infinite matrix equation arising therein. (Simple truncation to finite order is not good enough.) Our boundary conditions give rise to singularities which prevent other known methods (including the original form of Teodorescu's) from working. The solution reveals how surprisingly good an approximation its asymptotic forms near the corners and at infinity are in most of the flow field.

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