Two methods are employed in hydrodynamics, called the Eulerian and Lagrangian, although both are due originally to Leonhard Euler.
In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes.
The Lagrangian method being employed rarely, we shall confine ourselves to the Eulerian treatment.
The Lagrangian equations of motion are then of the type aj1~j+a1r~i+.
In such cases the boundary condition on the fluid uses the Lagrangian derivative.