SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 754-794, January 2021.
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.

中文翻译：

---

将不可压缩的理想流体从狭槽倾斜注入自由流

SIAM数学分析杂志，第53卷，第1期，第754-794页，2021年1月。
本文研究了缝膜冷却中的两相流体自由边界问题。对于在自由界面上具有跳跃关系的不可压缩的无粘性两相流体的存在和唯一性，我们给出了两个恰当的结果。该问题导致不可压缩的理想流体从狭槽倾斜注入自由流。从数学的角度来看，这项工作是由先驱工作[Arch。配给。机甲 A. Friedman的“ Anal。94（1986），第335--361页]，其中在某些特殊情况下获得了一些适定的结果。此外，A。Friedman在[工业问题中的数学，IMA第 数学。应用 16，斯普林格，纽约，1988]关于注入流问题的存在和唯一性的一般情况。