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Global regularity of solutions to the 2D steady compressible Prandtl equations

Authors :
Yonghui Zou
Source :
Communications in Analysis and Mechanics, Vol 15, Iss 4, Pp 695-715 (2023)
Publication Year :
2023
Publisher :
AIMS Press, 2023.

Abstract

In this paper, we study the global $ C^{\infty} $ regularity of solutions to the boundary layer equations for two-dimensional steady compressible flow under the favorable pressure gradient. To our knowledge, the difficulty of the proof is the degeneracy near the boundary. By using the regularity theory and maximum principles of parabolic equations together with the von Mises transformation, we give a positive answer to it. When the outer flow and the initial data satisfied appropriate conditions, we prove that Oleinik type solutions smooth up the boundary $ y = 0 $ for any $ x > 0 $.

Details

Language :
English
ISSN :
28363310
Volume :
15
Issue :
4
Database :
Directory of Open Access Journals
Journal :
Communications in Analysis and Mechanics
Publication Type :
Academic Journal
Accession number :
edsdoj.bc5cb79ef9dd4b719935d1f86ecdf508
Document Type :
article
Full Text :
https://doi.org/10.3934/cam.2023034?viewType=HTML