PreprintCC BY 4.0arXiv
The Three-Dimensional Divergence-Curl Problem with Homogeneous Boundary Conditions and Pseudo-Harmonic Fields
Abstract
This article addresses the solvability of the three-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.
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BibTeX
@misc{gorshkov2026threedimensional,
title = {{The Three-Dimensional Divergence-Curl Problem with Homogeneous Boundary Conditions and Pseudo-Harmonic Fields}},
author = {A. V. Gorshkov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.10422},
eprint = {2605.10422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10422},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Three-Dimensional Divergence-Curl Problem with Homogeneous Boundary Conditions and Pseudo-Harmonic Fields
AU - A. V. Gorshkov
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.10422
UR - https://arxiv.org/abs/2605.10422
AB - This article addresses the solvability of the three-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.
ER -