Oblique Injection of incompressible ideal fluid from a slot into a free stream

TL;DR

This paper establishes the existence and uniqueness of solutions for a two-phase free boundary problem modeling oblique injection of an ideal incompressible fluid, solving an open problem in fluid dynamics.

Contribution

It provides the first well-posedness results for the general case of the fluid injection problem, extending previous special case analyses.

Findings

Proved existence of solutions for the free boundary problem.

Proved uniqueness of solutions under certain conditions.

Extended mathematical understanding of fluid injection phenomena.

Abstract

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 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 [13] by A. Friedman, in which some well-posedness results are obtained in some special case. Furthermore, A. Friedman proposed an open problem in [14] on the existence and uniqueness of the injection flow problem for more general case. The main results in this paper solve the open problem and establish the well-posedness results on the physical problem.