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Singularities in a two-fluid medium. (English) Zbl 0533.76108
Summary: We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.

MSC:
76T99 Multiphase and multicomponent flows
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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