Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations
We survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [1], and the well-posedness of a linearized problem given in [2...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022021?viewType=HTML |
| _version_ | 1811251213559136256 |
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| author | Chengchun Hao Tao Luo |
| author_facet | Chengchun Hao Tao Luo |
| author_sort | Chengchun Hao |
| collection | DOAJ |
| description | We survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [1], and the well-posedness of a linearized problem given in [2] in general n-dimensions (n⩾2) when the Taylor sign condition is satisfied and the free boundaries are closed. |
| first_indexed | 2024-04-12T16:17:10Z |
| format | Article |
| id | doaj.art-2e7f4a16b3f64316a3d6a8de91cbf8e5 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T16:17:10Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-2e7f4a16b3f64316a3d6a8de91cbf8e52022-12-22T03:25:42ZengAIMS PressElectronic Research Archive2688-15942022-01-0130240442410.3934/era.2022021Some results on free boundary problems of incompressible ideal magnetohydrodynamics equationsChengchun Hao0Tao Luo11. HLM, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China2. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong KongWe survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [1], and the well-posedness of a linearized problem given in [2] in general n-dimensions (n⩾2) when the Taylor sign condition is satisfied and the free boundaries are closed.https://www.aimspress.com/article/doi/10.3934/era.2022021?viewType=HTMLfree boundary problemsincompressible ideal magnetohydrodynamics equationsill-posednesslinearized problemwell-posedness |
| spellingShingle | Chengchun Hao Tao Luo Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations Electronic Research Archive free boundary problems incompressible ideal magnetohydrodynamics equations ill-posedness linearized problem well-posedness |
| title | Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| title_full | Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| title_fullStr | Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| title_full_unstemmed | Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| title_short | Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| title_sort | some results on free boundary problems of incompressible ideal magnetohydrodynamics equations |
| topic | free boundary problems incompressible ideal magnetohydrodynamics equations ill-posedness linearized problem well-posedness |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022021?viewType=HTML |
| work_keys_str_mv | AT chengchunhao someresultsonfreeboundaryproblemsofincompressibleidealmagnetohydrodynamicsequations AT taoluo someresultsonfreeboundaryproblemsofincompressibleidealmagnetohydrodynamicsequations |