Global regularity of solutions to the 2D steady compressible Prandtl equations
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 the...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-10-01
|
| Series: | Communications in Analysis and Mechanics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2023034?viewType=HTML |
| _version_ | 1797361240806260736 |
|---|---|
| author | Yonghui Zou |
| author_facet | Yonghui Zou |
| author_sort | Yonghui Zou |
| collection | DOAJ |
| description | 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 $. |
| first_indexed | 2024-03-08T15:51:05Z |
| format | Article |
| id | doaj.art-bc5cb79ef9dd4b719935d1f86ecdf508 |
| institution | Directory Open Access Journal |
| issn | 2836-3310 |
| language | English |
| last_indexed | 2024-03-08T15:51:05Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj.art-bc5cb79ef9dd4b719935d1f86ecdf5082024-01-09T06:04:43ZengAIMS PressCommunications in Analysis and Mechanics2836-33102023-10-0115469571510.3934/cam.2023034Global regularity of solutions to the 2D steady compressible Prandtl equationsYonghui Zou 0School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P.R.ChinaIn 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 $.https://www.aimspress.com/article/doi/10.3934/cam.2023034?viewType=HTMLcompressible prandtl equationsglobal $ c^{\infty} $ regularityfavorable pressure |
| spellingShingle | Yonghui Zou Global regularity of solutions to the 2D steady compressible Prandtl equations Communications in Analysis and Mechanics compressible prandtl equations global $ c^{\infty} $ regularity favorable pressure |
| title | Global regularity of solutions to the 2D steady compressible Prandtl equations |
| title_full | Global regularity of solutions to the 2D steady compressible Prandtl equations |
| title_fullStr | Global regularity of solutions to the 2D steady compressible Prandtl equations |
| title_full_unstemmed | Global regularity of solutions to the 2D steady compressible Prandtl equations |
| title_short | Global regularity of solutions to the 2D steady compressible Prandtl equations |
| title_sort | global regularity of solutions to the 2d steady compressible prandtl equations |
| topic | compressible prandtl equations global $ c^{\infty} $ regularity favorable pressure |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2023034?viewType=HTML |
| work_keys_str_mv | AT yonghuizou globalregularityofsolutionstothe2dsteadycompressibleprandtlequations |