Abstract
AbstractWe present proofs for the existence of distributional potentials for distributional vector fields , that is, , where Ω is an open subset of . The hypothesis in these proofs is the compatibility condition for all , 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 satisfying to functions with . The results are applied to properties of Hilbert spaces of functions occurring in the treatment of the Stokes operator and the Navier–Stokes equations.
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