= Componentwise harmonic vector field
{title2=$\nabla^2\boldsymbol\Phi=0$}
A vector field in Euclidean space is componentwise harmonic when each Cartesian component is a <harmonic function>, equivalently its componentwise <Laplacian> vanishes. Constant and linear vector fields are examples, as are constant linear combinations of derivatives of $1/r$ away from the origin in three dimensions. Such fields supply the vector potentials in the <Papkovich–Neuber representation>. Componentwise harmonicity does not by itself require zero divergence or zero curl.
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