Existence and Uniqueness Results for Double-Free-Boundary Problems in Fluid Dynamics

TL;DR

This paper investigates the existence and uniqueness of solutions for a double-free-boundary problem in fluid dynamics, modeling a stream over a gravitational potential terrain, with generalizations of previous results.

Contribution

It provides a new proof for the existence of solutions and explores the uniqueness of these solutions in the context of fluid flow with free boundaries.

Findings

Existence of solutions is established under general conditions.

A new proof technique is introduced for the existence theorem.

The paper discusses conditions for the uniqueness of solutions.

Abstract

In two space dimensions, we study a general double-free-boundary problem which models a stream flowing through a gravitaional potentiay. ntial-energy terrain. The existence theorem generalizes (by a different proof) a result of A. Beurling. We study the uniqueness question kn two ways.