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

2025/07/30 by Morozov, Oleg I.
#Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2507.22578

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.

Citations

• Integrability structures of the (2+1)-dimensional Euler equation
• On recursion operators for symmetries of the Pavlov-Mikhalev equation
• Recursion operators in the cotangent covering of the rdDym equation

Related

• A simplification of the vorticity equation and an extension of the vorticity persistence theorem to three dimensions
• A different derivation of conservation laws for water waves
• General vorticity conservation
• Integrability structures of the (2+1)-dimensional Euler equation
• A note on the central-upwind scheme for nonlocal conservation laws