Laplacian vector field
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In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is described by the following differential equations:
Since the curl of v is zero, it follows that v can be expressed as the gradient of a scalar potential (see irrotational field) φ :
.
Then, since the divergence of v is also zero, it follows from equation (1) that
which is equivalent to
.
Therefore, the potential of a Laplacian field satisfies Laplace's equation.
