Metadata
shorthands: {}
aliases: [Fundamental theorem of vector calculus, Helmholtz decomposition]
created: 2021-10-21 19:36:13
modified: 2022-01-10 04:13:04
States that any sufficiently smooth, rapidly decaying vector field in 3D can be resolved into the sum of an irrational vector field (curl-free) and a solenoidal vector field (divergence-free).
Because an irrational field has a scalar potential and a solenoidal vector field has a vector potential, the statement is the following:
Where