Global regularity of the steady Prandtl equation with favorable pressure gradient

  • Yue Wang

    School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Zhifei Zhang

    School of Mathematical Sciences, Peking University, 100871, Beijing, China
Global $C^∞$ regularity of the steady Prandtl equation with favorable pressure gradient cover

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Abstract

In the case of favorable pressure gradient, Oleinik obtained the global-in- solutions to the steady Prandtl equations with low regularity (see Oleinik and Samokhin [9], P.21, Theorem 2.1.1). Due to the degeneracy of the equation near the boundary, the question of higher regularity of Oleinik's solutions remains open. See the local-in- higher regularity established by Guo and Iyer [5]. In this paper, we prove that Oleinik's solutions are smooth up to the boundary for any , using further maximum principle techniques. Moreover, since Oleinik only assumed low regularity on the data prescribed at , our result implies instant smoothness (in the steady case, is often considered as initial time).

Cite this article

Yue Wang, Zhifei Zhang, Global regularity of the steady Prandtl equation with favorable pressure gradient. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 6, pp. 1989–2004

DOI 10.1016/J.ANIHPC.2021.02.007