Editing Helmholtz decomposition (section)

=== Fluid dynamics ===

In [[fluid dynamics]], the Helmholtz projection plays an important role, especially for the solvability theory of the [[Navier-Stokes equations]]. If the Helmholtz projection is applied to the linearized incompressible Navier-Stokes equations, the [[Stokes flow|Stokes equation]] is obtained. This depends only on the velocity of the particles in the flow, but no longer on the static pressure, allowing the equation to be reduced to one unknown. However, both equations, the Stokes and linearized equations, are equivalent. The operator <math>P\Delta</math> is called the [[Stokes operator]].<ref name="chorin1990" />