Abstract

We will talk about the Prandtl system with initial data admitting nondegenerate critical points. For any index $\sigma \in [3/2,2]$, we obtain the local in time well-posedness in the space of Gevrey class $G^\sigma$ in the tangential variable and Sobolev class in the normal variable so that the monotonicity condition on the tangential velocity is not needed to overcome the loss of tangential derivative. This answers the open question raised in the paper of D. G\'{e}rard-Varet and N. Masmoudi [ Ann. Sci. \'{E}c. Norm. Sup\’{e}r. (4) 48 (2015), no. 6, 1273-1325], in which the case $\sigma=7/4$ is solved. Joint work with Tong Yang.