We present proofs for the existence of distributional potentials (Formula presented.) for distributional vector fields (Formula presented.), that is, (Formula presented.), where Ω is an open subset of (Formula presented.). The hypothesis in these proofs is the compatibility condition (Formula presented.) for all (Formula presented.), if Ω is simply connected, and a stronger condition in the general case. A key tool in our treatment is the Bogovskiĭ formula, assigning vector fields (Formula presented.) satisfying (Formula presented.) to functions (Formula presented.) with (Formula presented.). The results are applied to properties of Hilbert spaces of functions occurring in the treatment of the Stokes operator and the Navier–Stokes equations.