Global well-posedness for the 2D MHD equations with only vertical velocity damping term
This paper concerns two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations without magnetic diffusion with only vertical velocity damping term in the periodic domain. We prove the stability and decay rate for smooth solutions on perturbations near a background magnetic field of the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241725 |
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| author | Huan Long Suhui Ye |
| author_facet | Huan Long Suhui Ye |
| author_sort | Huan Long |
| collection | DOAJ |
| description | This paper concerns two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations without magnetic diffusion with only vertical velocity damping term in the periodic domain. We prove the stability and decay rate for smooth solutions on perturbations near a background magnetic field of the system under the assumptions that the initial magnetic field satisfies the Diophantine condition. |
| format | Article |
| id | doaj-art-5c6d3e9c1d0a4736990e339a4a991a00 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-5c6d3e9c1d0a4736990e339a4a991a002025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912363713638410.3934/math.20241725Global well-posedness for the 2D MHD equations with only vertical velocity damping termHuan Long0Suhui Ye1School of Mathematical Sciences, Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059, ChinaSchool of Mathematical Sciences, Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059, ChinaThis paper concerns two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations without magnetic diffusion with only vertical velocity damping term in the periodic domain. We prove the stability and decay rate for smooth solutions on perturbations near a background magnetic field of the system under the assumptions that the initial magnetic field satisfies the Diophantine condition.https://www.aimspress.com/article/doi/10.3934/math.20241725magnetohydrodynamic equationsglobal solutionsdiophantine condition |
| spellingShingle | Huan Long Suhui Ye Global well-posedness for the 2D MHD equations with only vertical velocity damping term AIMS Mathematics magnetohydrodynamic equations global solutions diophantine condition |
| title | Global well-posedness for the 2D MHD equations with only vertical velocity damping term |
| title_full | Global well-posedness for the 2D MHD equations with only vertical velocity damping term |
| title_fullStr | Global well-posedness for the 2D MHD equations with only vertical velocity damping term |
| title_full_unstemmed | Global well-posedness for the 2D MHD equations with only vertical velocity damping term |
| title_short | Global well-posedness for the 2D MHD equations with only vertical velocity damping term |
| title_sort | global well posedness for the 2d mhd equations with only vertical velocity damping term |
| topic | magnetohydrodynamic equations global solutions diophantine condition |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241725 |
| work_keys_str_mv | AT huanlong globalwellposednessforthe2dmhdequationswithonlyverticalvelocitydampingterm AT suhuiye globalwellposednessforthe2dmhdequationswithonlyverticalvelocitydampingterm |