Global C∞ 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-x 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-x 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 C∞ 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