  In this paper, we consider the 3D Prandtl equation in a periodic domain and
prove the local existence and uniqueness of solutions by the energy method in a
polynomial weighted Sobolev space. Compared to the existence and uniqueness of
solutions to the classical Prandtl equations where the Crocco transform has
always been used with the general outer flow $U\neq\text{constant}$, this
Crocco transform is not needed here for 3D Prandtl equations. We use the skill
of cancellation mechanism and construct a new unknown function to show that the
existence and uniqueness of solutions to 3D Prandtl equations (cf. Masmoudi and
Wong, Comm. Pure Appl. Math., 68(10)(2015), 1683-1741) which extends from the
two dimensional case in \cite {12} to the present three dimensional case with a
special structure.
