Global C ∞ regularity of the steady Prandtl equation with favorable pressure gradient
Wang, Yue1 ; Zhang, Zhifei2
1 a School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2 b School of Mathematical Sciences, Peking University, 100871, Beijing, China
Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1989-2004.
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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 y=0 for any x>0, using further maximum principle techniques. Moreover, since Oleinik only assumed low regularity on the data prescribed at x=0, our result implies instant smoothness (in the steady case, x=0 is often considered as initial time).

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DOI : 10.1016/j.anihpc.2021.02.007
Mots-clés : Global $ {C}^{\infty }$ regularity, Steady Prandtl equations, Favorable pressure gradient
Wang, Yue 1 ; Zhang, Zhifei 2

1 a School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2 b School of Mathematical Sciences, Peking University, 100871, Beijing, China 
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Wang, Yue; Zhang, Zhifei. Global C
               ∞ regularity of the steady Prandtl equation with favorable pressure gradient. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1989-2004. doi : 10.1016/j.anihpc.2021.02.007. http://www.numdam.org/articles/10.1016/j.anihpc.2021.02.007/

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