On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910209025245184 |
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| author | Gorshkov, A. V. |
| author_facet | Gorshkov, A. V. |
| contents | This article addresses the solvability of the multi-dimensional divergence-curl problem with a no-slip boundary condition. A solvability criterion is derived as an orthogonality condition of the vorticity function to pseudo-harmonic fields. A countable family of such fields, sufficient for the solvability of the three-dimensional problem in the exterior of a sphere, is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10422 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields Gorshkov, A. V. Analysis of PDEs 35A01, 33C55, 35J05 This article addresses the solvability of the multi-dimensional divergence-curl problem with a no-slip boundary condition. A solvability criterion is derived as an orthogonality condition of the vorticity function to pseudo-harmonic fields. A countable family of such fields, sufficient for the solvability of the three-dimensional problem in the exterior of a sphere, is also presented. |
| title | On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields |
| topic | Analysis of PDEs 35A01, 33C55, 35J05 |
| url | https://arxiv.org/abs/2605.10422 |