 The key requirement for lubrication theory is that the ratio formula_3 is small, that is, formula_4.The Navier–Stokes equations (or Stokes equations, when fluid inertia may be neglected) are expanded in this small parameter, and the leading-order equations are then

where formula_6 and formula_7 are coordinates in the direction of the substrate and perpendicular to it respectively.Here formula_8 is the fluid pressure, and formula_9 is the fluid velocity component parallel to the substrate; formula_10 is the fluid viscosity.