Boundary value problems for two dimensional steady incompressible fluids

TL;DR

This paper investigates the solvability of boundary value problems for 2D steady incompressible Euler equations, analyzing the applicability of the Grad-Shafranov and vorticity transport methods to solutions with non-zero vorticity.

Contribution

It clarifies the conditions under which these two main methods can be applied to solve boundary value problems in this context.

Findings

Identifies boundary conditions suitable for each method.

Describes solutions with non-zero vorticity.

Provides criteria for method applicability.

Abstract

In this paper we study the solvability of different boundary value problems for the two dimensional steady incompressible Euler equation. Two main methods are currently available to study those problems, namely the Grad-Shafranov method and the vorticity transport method. We describe for which boundary value problems these methods can be applied. The obtained solutions have non-vanishing vorticity.