Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points

  • Wei-Xi Li

    Wuhan University, China
  • Tong Yang

    Jinan University, Guangzhou, China, and City University of Hong Kong, Hong Kong
Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points cover
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Abstract

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 by D. Gérard-Varet and N. Masmoudi [Ann. Sci. École Norm. Sup. (4) 48 (2015), no. 6, 1273–1325], who solved the case σ=7/4\sigma=7/4.

Cite this article

Wei-Xi Li, Tong Yang, Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points. J. Eur. Math. Soc. 22 (2020), no. 3, pp. 717–775

DOI 10.4171/JEMS/931