  The well-posedness of the three space dimensional Prandtl equations is
studied under some constraint on its flow structure. It reveals that the
classical Burgers equation plays an important role in determining this type of
flow with special structure, that avoids the appearance of the complicated
secondary flow in the three-dimensional Prandtl boundary layers. And the
sufficiency of the monotonicity condition on the tangential velocity field for
the existence of solutions to the Prandtl boundary layer equations is
illustrated in the three dimensional setting. Moreover, it is shown that this
structured flow is linearly stable for any three-dimensional perturbation.
