Boundary-layer equation ($u{u}_x+v{u}_y=-P_x/\rho +\nu u_{yy},u_x+v_y=0$)

The leading momentum and mass equations in a thin laminar shear region with flow predominantly along a surface or jet axis. Longitudinal viscous derivatives are smaller than transverse ones, and pressure is supplied by the outer flow. The transverse velocity remains necessary for mass conservation and entrainment even when it is small compared with the axial velocity.