Continuity equation

$\partial\rho/\partial t + \nabla\cdot(\rho\mathbf{v}) = 0$ -- the local statement that a conserved quantity is neither created nor destroyed.

A continuity equation $\partial\rho/\partial t + \nabla\cdot(\rho\mathbf{v})=0$ is the local, differential statement of a global conservation law -- whatever quantity $\rho$ is being tracked changes at a point only by flowing in or out, never by being created or destroyed there.

Examples

Mass, charge, and probability density each satisfy their own continuity equation in the appropriate physical theory.