Helmholtz's theorems
In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex lines. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored. Helmholtz's three theorems are as follows:

Helmholtz's first theorem

The strength of a vortex line is constant along its length. Helmholtz's second theorem

A vortex line cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path. Helmholtz's third theorem

A fluid element that is initially irrotational remains irrotational.