C^{2} formulation of Euler fluid

TL;DR

This paper develops a Hamiltonian formalism for Euler fluid dynamics using a C^2 phase space representation, providing a new mathematical framework for analyzing fluid behavior.

Contribution

It introduces a novel C^2 formulation of Euler fluid equations within the Hamiltonian formalism, expanding the mathematical tools available for fluid dynamics analysis.

Findings

Provides a new Hamiltonian framework for Euler fluids

Enables advanced mathematical analysis of fluid behavior

Lays groundwork for future theoretical developments

Abstract

The Hamiltonian formalism for the continuous media is constructed using the representation of Euler variables in $\mathcal{C}^{2}\times \infty$ phase space.