A study of the Prandtl Batchelor problem using variational method

TL;DR

This paper explores the existence of solutions to the Prandtl-Batchelor free boundary problem using variational and algebraic topology methods, improving classical results in the field.

Contribution

It introduces a combined variational and algebraic topology approach to establish solution existence for nonlinear elliptic free boundary problems.

Findings

Existence of nontrivial weak solutions proven

Improved classical results on Prandtl-Batchelor problems

Application of variational techniques to free boundary problems

Abstract

In this paper, we investigate the existence of nontrivial weak solutions for the Prandtl-Batchelor type free boundary value elliptic problem driven by a power nonlinearity. The algebraic topology approach will be used to establish the existence of solutions of approximate problem, while variational techniques will be used to determine the existence of major problem solutions. In the process several classical results are improved.