 Helmholtz decomposition

The Helmholtz decomposition separates a vector field into a gradient field and a field with zero divergence. The precise function spaces, boundary conditions and decay hypotheses determine existence and uniqueness. In the square-integrable bounded-domain formulation, the solenoidal component is selected by the Leray-Helmholtz projection.

Helmholtz decomposition is a theorem in vector calculus that states that any sufficiently smooth, rapidly decaying vector field in three-dimensional space can be uniquely expressed as the sum of two components: a gradient of a scalar potential (irrotational part) and the curl of a vector potential (solenoidal part).