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

Yonghui Zou; Yonghui Zou

doi:10.3934/cam.2023034

Communications in Analysis and Mechanics

2023, Volume 15, Issue 4: 695-715. doi: 10.3934/cam.2023034

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Research article

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

Yonghui Zou ^,

School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P.R.China

Received: 16 August 2023 Revised: 22 October 2023 Accepted: 23 October 2023 Published: 27 October 2023
35Q30, 76D10, 76N20

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 $.
- compressible Prandtl equations,
- global $ C^{\infty} $ regularity,
- favorable pressure
Citation: Yonghui Zou. Global regularity of solutions to the 2D steady compressible Prandtl equations[J]. Communications in Analysis and Mechanics, 2023, 15(4): 695-715. doi: 10.3934/cam.2023034

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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 $.

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