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On a free boundary problem in fluid mechanics. (English) Zbl 0719.76011

The paper deals with the two-dimensional steady irrotational flow of an incompressible inviscid fluid jet exiting from a small opening of a nozzle and moving towards a permeable wall. The flow region is bounded by the mouth of the nozzle, the free boundaries and the porous wall. The author investigates the physical problem by transforming it into a minimum problem for the stream function and proves the existence and uniqueness of the solution of the minimum problem. Supplementary results concerning the shape of the flow region, the properties of the velocity and the monotonicity of the stream function are established.
Finally, the author presents some numerical results employing a finite element method and investigates the dependence of the streamline function and of the free boundaries of the jet on the two given velocities (the normal velocity on the mouth of the nozzle and the normal velocity on the porous wall).

MSC:

76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76M30 Variational methods applied to problems in fluid mechanics
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