In this talk,we will present some recent joint works with Chengjie Liu and YaguangWang on the well-posedness theories of the Prandtl layer equations.Firstly,the Prandtl equations in three space variables are studied both locally and globally in time under some constraint on its flow structure.It reveals that the classical Burgers equation plays an important role in the analysis.And the monotonicity condition on the velocity and the favorable condition on pressure are illustrated in the 3D setting.Further,the linear stability of this structured flow is justified.Finally,we will present some related study on the compressible flow.