Editing Continuity equation (section)

===Differential form===
{{see also|Conservation law|conservation form}}
By the [[divergence theorem]], a general continuity equation can also be written in a "differential form":
{{Equation box 1
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|equation=<math>\frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{j} = \sigma</math>
|cellpadding
|border
|border colour = #0073CF
|background colour=#F5FFFA
}}
where
* {{math|∇⋅}} is [[divergence]],
* {{math|''ρ''}} is the density of the amount {{math|''q''}} (i.e. the quantity {{math|''q''}} per unit volume),
* {{math|'''j'''}} is the flux of {{math|''q''}} (i.e. '''j''' = ρ'''v''', where '''v''' is the vector field describing the movement of the quantity {{math|''q''}}),
* {{math|''t''}} is time,
* {{math|''σ''}} is the generation of {{math|''q''}} per unit volume per unit time. Terms that generate {{math|''q''}} (i.e., {{math|''σ'' > 0}}) or remove {{math|''q''}} (i.e., {{math|''σ'' < 0}}) are referred to as [[sources and sinks]] respectively.

This general equation may be used to derive any continuity equation, ranging from as simple as the volume continuity equation to as complicated as the [[Navier–Stokes equations]]. This equation also generalizes the [[advection equation]]. Other equations in physics, such as [[Gauss's law|Gauss's law of the electric field]] and [[Gauss's law for gravity]], have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because {{math|'''j'''}} in those cases does not represent the flow of a real physical quantity.

In the case that {{math|''q''}} is a [[Conservation law (physics)|conserved quantity]] that cannot be created or destroyed (such as [[energy]]), {{math|1=''σ'' = 0}} and the equations become:
<math display="block">\frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{j} = 0</math>