IEVref: 102-05-29 ID: Language: en Status: Standard Term: Laplacian, Synonym1: Synonym2: Synonym3: Symbol: Definition: vector ΔU associated at each point of a given space region with a vector U, equal to the gradient of the divergence of the vector field minus the rotation of the rotation of this vector field ΔU = grad div U − rot rot UNote 1 to entry: In orthonormal Cartesian coordinates, the three components of the Laplacian of a vector field are: $\frac{{\partial }^{2}{U}_{x}}{\partial \text{\hspace{0.17em}}{x}^{2}}+\frac{{\partial }^{2}{U}_{x}}{\partial \text{\hspace{0.17em}}{y}^{2}}+\frac{{\partial }^{2}{U}_{x}}{\partial \text{\hspace{0.17em}}{z}^{2}}\text{\hspace{0.17em}}\text{\hspace{0.17em}},\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{{\partial }^{2}{U}_{y}}{\partial \text{\hspace{0.17em}}{x}^{2}}+\frac{{\partial }^{2}{U}_{y}}{\partial \text{\hspace{0.17em}}{y}^{2}}+\frac{{\partial }^{2}{U}_{y}}{\partial \text{\hspace{0.17em}}{z}^{2}}\text{\hspace{0.17em}}\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\frac{{\partial }^{2}{U}_{z}}{\partial \text{\hspace{0.17em}}{x}^{2}}+\frac{{\partial }^{2}{U}_{z}}{\partial \text{\hspace{0.17em}}{y}^{2}}+\frac{{\partial }^{2}{U}_{z}}{\partial \text{\hspace{0.17em}}{z}^{2}}$. Note 2 to entry: The Laplacian of the vector field U is denoted by ΔU or ∇2U, where Δ is the Laplacian operator. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: