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.
|Original language||English (US)|
|Number of pages||53|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Nov 1 2015|
ASJC Scopus subject areas