Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations
In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/5343824 |
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| author | Eunji Jeong Junha Kim Jihoon Lee |
| author_facet | Eunji Jeong Junha Kim Jihoon Lee |
| author_sort | Eunji Jeong |
| collection | DOAJ |
| description | In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without resistivity. Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations. |
| format | Article |
| id | doaj-art-89162640b2fa42fbac5737bf5fbc8db4 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-89162640b2fa42fbac5737bf5fbc8db42025-02-03T05:48:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/53438245343824Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD EquationsEunji Jeong0Junha Kim1Jihoon Lee2Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of KoreaDepartment of Mathematics, Chung-Ang University, Seoul 06974, Republic of KoreaDepartment of Mathematics, Chung-Ang University, Seoul 06974, Republic of KoreaIn this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without resistivity. Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations.http://dx.doi.org/10.1155/2018/5343824 |
| spellingShingle | Eunji Jeong Junha Kim Jihoon Lee Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations Advances in Mathematical Physics |
| title | Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations |
| title_full | Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations |
| title_fullStr | Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations |
| title_full_unstemmed | Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations |
| title_short | Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations |
| title_sort | local well posedness and blow up for the solutions to the axisymmetric inviscid hall mhd equations |
| url | http://dx.doi.org/10.1155/2018/5343824 |
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