Linked from

The 29 pages that link to Divergence, each with the reason it gives.

• Maxwell's equationsRelated: The two Gauss laws state the divergences of the electric and magnetic fields.

• Continuity equationRelated: Velocity divergence represents local expansion or contraction in the flow.

• Vector fieldRelated: It detects local sources and sinks in the field.

• GradientCompared with: Unlike the gradient, divergence takes a vector field as input and returns a scalar.

• Poisson's equationRelated: The Laplacian can be expressed as the divergence of a gradient.

• Covariant derivativeRelated: The covariant derivative contracts to define divergence on curved manifolds.

• Incompressible flowBroader topic: Its value for the velocity field distinguishes local expansion from incompressible motion.

• LaplacianRelated: Applying divergence to the gradient produces the Laplacian.

• Velocity fieldRelated: The velocity field’s divergence indicates local expansion or compression of the medium.

• Divergence theoremBroader topic: The theorem integrates this local measure throughout the enclosed volume.

• Green's theoremRelated: The flux form integrates divergence over the region to recover boundary flux.

• CurlCompared with: Divergence measures sources and sinks, while curl measures local circulation.

• Eulerian descriptionRelated: Spatial derivatives such as divergence describe local expansion or compression of flow.

• Vector calculusBroader topic: It detects sources and sinks in a field.

• Diffusion equationRelated: Taking the divergence of diffusive flux converts transport into a local concentration change.

• Exterior derivativeBroader topic: With a volume form, the derivative of a corresponding 2-form encodes divergence.

• MagnetostaticsRelated: Zero magnetic divergence expresses the absence of isolated magnetic charges.

• Electric fluxRelated: The divergence theorem relates electric flux through a closed surface to divergence inside it.

• Gauss's law for magnetismRelated: The law’s differential form says the divergence of the magnetic field vanishes everywhere.

• Magnetic vector potentialRelated: The zero divergence of magnetic fields permits a vector-potential description in suitable domains.

• Cauchy momentum equationRelated: Applied to stress, it gives the local resultant of internal forces.

• SourceRelated: Positive divergence is the local mathematical signature of a source.

• Solenoidal vector fieldNarrower topic: A solenoidal field is defined by divergence being zero at every point.

• Helmholtz decompositionRelated: The decomposition separates out a component whose divergence vanishes.

• Bendixson–Dulac theoremRelated: The theorem tests whether the vector field’s weighted divergence keeps one strict sign.

• Eulerian flow fieldRelated: Velocity divergence indicates local expansion or compression in the flow.

• Field lineRelated: Divergence helps determine whether field lines appear to originate or terminate locally.

• Jacobian matrix and determinantCompared with: Divergence is a trace of a vector field’s Jacobian, not its determinant.

• Liouville's formulaRelated: In linear systems, the coefficient matrix's trace is the vector field's divergence.