codifferential

In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as ∂ₜ𝜔+ℒᵤ𝜔=0\u=𝛿̃𝜂⁻¹𝛥⁻¹𝜔 where 𝜔 is the vorticity 2-form, ℒᵤ denotes the Lie derivative with respect to the velocity field u, 𝛥 is the Hodge Laplacian, 𝛿 is the codifferential (the negative of the divergence operator), and ̃𝜂⁻¹ is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric 𝜂.

One important concept is the introduction of codifferential operator