A harmonic maps approach to fluid flows

TL;DR

This paper classifies all two-dimensional ideal fluid flows with harmonic Lagrangian maps, providing explicit solutions to the incompressible Euler equations in Lagrangian form, advancing the understanding of fluid dynamics.

Contribution

It offers a complete classification and explicit solutions for 2D ideal fluid flows with harmonic Lagrangian maps, a novel approach in fluid dynamics.

Findings

Explicit solutions to 2D Euler equations with harmonic Lagrangian maps

Complete classification of such fluid flows

Advancement in understanding Lagrangian fluid dynamics

Abstract

We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the incompressible two-dimensional Euler equations (in Lagrangian variables).