Special Properties of Plane Solenoidal Fields
Algebraic and integral identities have been obtained for a pair or a triple of plane solenoidal fields. We obtain sufficient potentiality conditions for a plane vector field. The integral identities are also important for exact a priori estimates.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-08-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/16/1863 |
| _version_ | 1797523054458306560 |
|---|---|
| author | Vladimir I. Semenov |
| author_facet | Vladimir I. Semenov |
| author_sort | Vladimir I. Semenov |
| collection | DOAJ |
| description | Algebraic and integral identities have been obtained for a pair or a triple of plane solenoidal fields. We obtain sufficient potentiality conditions for a plane vector field. The integral identities are also important for exact a priori estimates. |
| first_indexed | 2024-03-10T08:37:59Z |
| format | Article |
| id | doaj.art-4ef76664ee4f4723994da0b13f69d131 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:59Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4ef76664ee4f4723994da0b13f69d1312023-11-22T08:33:03ZengMDPI AGMathematics2227-73902021-08-01916186310.3390/math9161863Special Properties of Plane Solenoidal FieldsVladimir I. Semenov0Institute Physics, Mathematics and Computer Sciences, Baltic Federal University, 236016 Kaliningrad, RussiaAlgebraic and integral identities have been obtained for a pair or a triple of plane solenoidal fields. We obtain sufficient potentiality conditions for a plane vector field. The integral identities are also important for exact a priori estimates.https://www.mdpi.com/2227-7390/9/16/1863solenoidal fieldpotential fieldHelmholmtz–Weyl decomposition |
| spellingShingle | Vladimir I. Semenov Special Properties of Plane Solenoidal Fields Mathematics solenoidal field potential field Helmholmtz–Weyl decomposition |
| title | Special Properties of Plane Solenoidal Fields |
| title_full | Special Properties of Plane Solenoidal Fields |
| title_fullStr | Special Properties of Plane Solenoidal Fields |
| title_full_unstemmed | Special Properties of Plane Solenoidal Fields |
| title_short | Special Properties of Plane Solenoidal Fields |
| title_sort | special properties of plane solenoidal fields |
| topic | solenoidal field potential field Helmholmtz–Weyl decomposition |
| url | https://www.mdpi.com/2227-7390/9/16/1863 |
| work_keys_str_mv | AT vladimirisemenov specialpropertiesofplanesolenoidalfields |