OBLIQUE INJECTION OF INCOMPRESSIBLE IDEAL FLUID FROM A SLOT INTO A FREE STREAM

This paper deals with a two-phase fluid free boundary problem in a slot-film cooling. We give two well-posedness results on the existence and uniqueness of the incompressible inviscid two-phase fluid with a jump relation on a free interface. The problem formulates the oblique injection of an incompressible ideal fluid from a slot into a free stream. From the mathematical point of view, this work is motivated by the pioneer work [Arch. Ration. Mech. Anal., 94 (1986), pp. 335-361] by A. Friedman, in which some well-posedness results are obtained in some special case. Furthermore, A. Friedman proposed an open problem in [Mathematics in Industrial Problems, IMA Vol. Math. Appl. 16, Springer, New York, 1988] on the existence and uniqueness of the injection flow problem for the more general case. The main results in this paper solve the open problem and establish the well-posedness results on the physical problem.