Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space
The purpose of this paper is to prove the well-posedness of the 2D magnetohydrodynamic (MHD) boundary layer equations for small initial data in Sobolev space of polynomial weight and low regularity. Our proofs are based on the paralinearization method and an abstract bootstrap argument. We first obt...
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AIMS Press
2024-12-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024309 |
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| author | Xiaolei Dong |
| author_facet | Xiaolei Dong |
| author_sort | Xiaolei Dong |
| collection | DOAJ |
| description | The purpose of this paper is to prove the well-posedness of the 2D magnetohydrodynamic (MHD) boundary layer equations for small initial data in Sobolev space of polynomial weight and low regularity. Our proofs are based on the paralinearization method and an abstract bootstrap argument. We first obtain the systems (3.3)–(3.6) by paralinearizing and symmetrizing the system (1.2). Then, we establish the estimates of the solution in horizontal direction and vertical direction, respectively. Finally, we prove the well-posedness of the 2D MHD boundary layer equations by an abstract bootstrap argument. |
| format | Article |
| id | doaj-art-26d1bba05466472a923249c0d4595bb0 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-26d1bba05466472a923249c0d4595bb02025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126618664010.3934/era.2024309Well-posedness of the MHD boundary layer equations with small initial data in Sobolev spaceXiaolei Dong0School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, ChinaThe purpose of this paper is to prove the well-posedness of the 2D magnetohydrodynamic (MHD) boundary layer equations for small initial data in Sobolev space of polynomial weight and low regularity. Our proofs are based on the paralinearization method and an abstract bootstrap argument. We first obtain the systems (3.3)–(3.6) by paralinearizing and symmetrizing the system (1.2). Then, we establish the estimates of the solution in horizontal direction and vertical direction, respectively. Finally, we prove the well-posedness of the 2D MHD boundary layer equations by an abstract bootstrap argument.https://www.aimspress.com/article/doi/10.3934/era.20243092d mhd boundary layer equationspolynomial weightwell-posednessbootstrap argumentparalinearization method |
| spellingShingle | Xiaolei Dong Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space Electronic Research Archive 2d mhd boundary layer equations polynomial weight well-posedness bootstrap argument paralinearization method |
| title | Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space |
| title_full | Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space |
| title_fullStr | Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space |
| title_full_unstemmed | Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space |
| title_short | Well-posedness of the MHD boundary layer equations with small initial data in Sobolev space |
| title_sort | well posedness of the mhd boundary layer equations with small initial data in sobolev space |
| topic | 2d mhd boundary layer equations polynomial weight well-posedness bootstrap argument paralinearization method |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024309 |
| work_keys_str_mv | AT xiaoleidong wellposednessofthemhdboundarylayerequationswithsmallinitialdatainsobolevspace |