On a prolongation construction for local non-divergent vector fields on R<sup>n</sup>
The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This co...
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| Format: | Article |
| Language: | Russian |
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Moscow State Technical University of Civil Aviation
2016-11-01
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| Series: | Научный вестник МГТУ ГА |
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| Online Access: | https://avia.mstuca.ru/jour/article/view/309 |
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| _version_ | 1849252784955719680 |
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| author | A. M. Lukatsky |
| author_facet | A. M. Lukatsky |
| author_sort | A. M. Lukatsky |
| collection | DOAJ |
| description | The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups. |
| format | Article |
| id | doaj-art-38e1ce29061e444ca8e5b0e67e7c67d9 |
| institution | Kabale University |
| issn | 2079-0619 2542-0119 |
| language | Russian |
| publishDate | 2016-11-01 |
| publisher | Moscow State Technical University of Civil Aviation |
| record_format | Article |
| series | Научный вестник МГТУ ГА |
| spelling | doaj-art-38e1ce29061e444ca8e5b0e67e7c67d92025-08-20T03:56:33ZrusMoscow State Technical University of Civil AviationНаучный вестник МГТУ ГА2079-06192542-01192016-11-012208894309On a prolongation construction for local non-divergent vector fields on R<sup>n</sup>A. M. Lukatsky0(ИНЭИ) РАНThe problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.https://avia.mstuca.ru/jour/article/view/309locally non-divergent vector fieldsmooth prolongationideal incompressible fluideuler equationsfinite vector fieldlie algebras |
| spellingShingle | A. M. Lukatsky On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> Научный вестник МГТУ ГА locally non-divergent vector field smooth prolongation ideal incompressible fluid euler equations finite vector field lie algebras |
| title | On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> |
| title_full | On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> |
| title_fullStr | On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> |
| title_full_unstemmed | On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> |
| title_short | On a prolongation construction for local non-divergent vector fields on R<sup>n</sup> |
| title_sort | on a prolongation construction for local non divergent vector fields on r sup n sup |
| topic | locally non-divergent vector field smooth prolongation ideal incompressible fluid euler equations finite vector field lie algebras |
| url | https://avia.mstuca.ru/jour/article/view/309 |
| work_keys_str_mv | AT amlukatsky onaprolongationconstructionforlocalnondivergentvectorfieldsonrsupnsup |