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Séminaire de EDP - Physique Mathématique

Well-posedness in Gevrey Function space for the Prandtl equations with non-degenerate critical points

Wei-Xi Li

( Wuhan University )

Salle 2

le 26 octobre 2016 à 11:00

In the talk, we study the well-posedness of the Prandtl system without monotonicity and analyticity assumption. Precisely, for any index σ[3/2,2],\sigma\in[3/2, 2], we obtain the local in time well-posedness in the space of Gevrey class GσG^\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. Gérard-Varet and N. Masmoudi (Ann. Sci. Ec. Norm. Supér. (4) 48 (2015), no. 6, 1273-1325), in which the case σ=7/4\sigma=7/4 is solved.