Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab
In this paper, we study Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab. We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular comp...
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| Veröffentlicht in: | Journal of mathematical physics 2021-07, Vol.62 (7) |
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| container_title | Journal of mathematical physics |
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| creator | Pan, Xinghong |
| description | In this paper, we study Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab. We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular component(s) of the velocity or (and) the magnetic field is (are) axially symmetric is needed. More precisely, five types of boundary conditions will be considered: the vertical periodic boundary condition for the velocity and the magnetic field, the Navier-slip boundary condition for the velocity, the perfectly conducting or insulating boundary condition for the magnetic field, the non-slip boundary condition for the velocity, and the perfectly conducting or insulating boundary condition for the magnetic field. One of our innovations is that we do not impose finite Dirichlet integral assumption on the magnetic field compared with previous works. |
| doi_str_mv | 10.1063/5.0031564 |
| format | Article |
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We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular component(s) of the velocity or (and) the magnetic field is (are) axially symmetric is needed. More precisely, five types of boundary conditions will be considered: the vertical periodic boundary condition for the velocity and the magnetic field, the Navier-slip boundary condition for the velocity, the perfectly conducting or insulating boundary condition for the magnetic field, the non-slip boundary condition for the velocity, and the perfectly conducting or insulating boundary condition for the magnetic field. 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We will prove trivialness of the velocity and the magnetic field with various boundary conditions. In some boundary conditions, the additional assumption that the horizontal angular component(s) of the velocity or (and) the magnetic field is (are) axially symmetric is needed. More precisely, five types of boundary conditions will be considered: the vertical periodic boundary condition for the velocity and the magnetic field, the Navier-slip boundary condition for the velocity, the perfectly conducting or insulating boundary condition for the magnetic field, the non-slip boundary condition for the velocity, and the perfectly conducting or insulating boundary condition for the magnetic field. One of our innovations is that we do not impose finite Dirichlet integral assumption on the magnetic field compared with previous works.</description><subject>Angular velocity</subject><subject>Boundary conditions</subject><subject>Dirichlet problem</subject><subject>Electrons</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Liouville theorem</subject><subject>Magnetic fields</subject><subject>Magnetism</subject><subject>Magnetohydrodynamics</subject><subject>Physics</subject><subject>Slip</subject><subject>Velocity</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNqd0EtLxDAQAOAgCq6rB_9BwJNC10ma1x5lfcKCFwVvIW0Tt0vbrEm60H9vly549zQM880MMwhdE1gQEPk9XwDkhAt2gmYE1DKTgqtTNAOgNKNMqXN0EeMWgBDF2Ax9rWvf7-umsThtrA-2xd7hxyz6pk-17yJO_lDBMZlDbsKAW_Pd2eQ3QxV8NXSmrcuI4xDT2Fx32ODYmOISnTnTRHt1jHP0-fz0sXrN1u8vb6uHdVZSLlPGpHFcFrxijigFhMvcSLUEWxYORCWIckubq4IKI5gqqoJzJqsiJ1QI5wTN5-hmmrsL_qe3Memt70M3rtR0pIQDcDKq20mVwccYrNO7ULfjMZqAPjxOc3183GjvJhvLejr6f3jvwx_Uu8rlv2uxfC4</recordid><startdate>20210701</startdate><enddate>20210701</enddate><creator>Pan, Xinghong</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-9715-9506</orcidid></search><sort><creationdate>20210701</creationdate><title>Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab</title><author>Pan, Xinghong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c257t-47af57b5d4f18801573a7890ecbf06d618f9e38b26a648bdb5547db31266ff623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Angular velocity</topic><topic>Boundary conditions</topic><topic>Dirichlet problem</topic><topic>Electrons</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Liouville theorem</topic><topic>Magnetic fields</topic><topic>Magnetism</topic><topic>Magnetohydrodynamics</topic><topic>Physics</topic><topic>Slip</topic><topic>Velocity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pan, Xinghong</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pan, Xinghong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab</atitle><jtitle>Journal of mathematical physics</jtitle><date>2021-07-01</date><risdate>2021</risdate><volume>62</volume><issue>7</issue><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>In this paper, we study Liouville theorems of D-solutions to the stationary magnetohydrodynamic system in a slab. 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| ispartof | Journal of mathematical physics, 2021-07, Vol.62 (7) |
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| language | eng |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Angular velocity Boundary conditions Dirichlet problem Electrons Fluid dynamics Fluid flow Liouville theorem Magnetic fields Magnetism Magnetohydrodynamics Physics Slip Velocity |
| title | Liouville theorem of D-solutions to the stationary magnetohydrodynamics system in a slab |
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