Laplacian vector field Guide, Meaning , Facts, Information and Description

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.

See also: potential flow, harmonic function

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