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In this paper we study the motion of an internal water wave and an internalwave in a porous medium. For these problems we establish that, if the freeboundary and, in the case of the Euler equations, also the tangential velocityat the interface are sufficiently smooth, the depth cannot vanish in finitetime. This results holds regardless of gravity and surface tension effects or,if applicable, the stratification in multiphase flows.

A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows