Abstract
A free boundary problem arising in a model for inviscid, incompressible shallow water entry at small deadrise angles is derived and analysed. The relationship between this novel free boundary problem and the well-known viscous squeeze film problem is described. An inverse method is used to construct explicit solutions for certain body profiles and to find criteria under which the splash sheet can `split'. A variational inequality formulation, conservation of certain generalized moments and the Schwarz function formulation are introduced.
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