  It has been thought for a while that the Prandtl system is only well-posed
under the Oleinik monotonicity assumption or under an analyticity assumption.
We show that the Prandtl system is actually locally well-posed for data that
belong to the Gevrey class 7/4 in the horizontal variable x. Our result
improves the classical local well-posedness result for data that are analytic
in x (that is Gevrey class 1). The proof uses new estimates, based on
non-quadratic energy functionals.
