Nonlocal conservation laws for the two-dimensional Euler equation in vorticity form

TL;DR

This paper derives a set of nonlocal conservation laws for the 2D Euler equation in vorticity form using canonical conservation laws and nonlocal cosymmetry, facilitated by a complex rotation of variables.

Contribution

It introduces a novel method combining canonical conservation laws and nonlocal cosymmetry to find nonlocal conservation laws for the 2D Euler equation.

Findings

Derived new nonlocal conservation laws for 2D Euler in vorticity form

Utilized complex rotation for computational simplicity

Enhanced understanding of conservation properties in fluid dynamics

Abstract

We combine the construction of the canonical conservation law and the nonlocal cosymmetry to derive a collection of nonlocal conservation laws for the two-dimensional Euler equation in vorticity form. For computational convenience and simplicity of presentation of the results we perform a complex rotation of the independent variables.