A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation

Anping Pan

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arXiv · 2512.03246

A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation

Anping Pan

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Abstract

In this paper, we study the inhomogeneous incompressible Euler equation (IIE in short) from a Lagrangian perspective. We establish a geodesic description of this equation and discuss the associated geometric structures. We also find the derivation of IIE from the Hamilton-Pontryagin action principle and derive the corresponding Lagrangian formulation. A byproduct is a new vorticity formulation of IIE. We also prove the Lagrangian analyticity of IIE using our Lagrangian representation formula.

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Anping Pan. 2025-12-02. A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation. https://arxiv.org/abs/2512.03246

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