  We prove local existence and uniqueness for the two-dimensional Prandtl
system in weighted Sobolev spaces under the Oleinik's monotonicity assumption.
In particular we do not use the Crocco transform. Our proof is based on a new
nonlinear energy estimate for the Prandtl system. This new energy estimate is
based on a cancellation property which is valid under the monotonicity
assumption. To construct the solution, we use a regularization of the system
that preserves this nonlinear structure. This new nonlinear structure may give
some insight on the convergence properties from Navier-Stokes system to Euler
system when the viscosity goes to zero.
