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Some existence result for a Stokes flow between two arbitrarily closed curves
Arch. Mech. 48 (6), 973-984, 1996
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Abstract
The problem of determining the slow viscous flow of a fluid between two arbitrarily closed curves is formulated as a system of Fredholm integral equations of the second kind, addying a pair of singularities located outside of the flow region. We show that the integral equations proposed here have a unique continuous solution, when the two closed curves are Lyapunov curves and the fluid velocity is continuous on these curves.