A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation

2025/12/02 by Pan, Anping
Mathematics · Physics and Astronomy · Engineering · #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.03246

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.

Citations

• Geometric blow-up criteria for the non-homogeneous incompressible Euler equations in 2-D
• Invertibility of a linearized Boussinesq flow: a symbolic approach
• Mechanisms of Lagrangian analyticity in fluids
• Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models
• On stationary solutions of two-dimensional Euler Equation
• On the Analyticity of Particle Trajectories in the Ideal Incompressible Fluid
• A Stochastic Representation for Backward Incompressible Navier-Stokes Equations
• An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

Related

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• 3D incompressible Euler: Geometric formalism and a hypothetical self-similar flow
• The Euler-Poincare Equations in Geophysical Fluid Dynamics