On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields
偏微分方程分析
2026-05-12 v1
摘要
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.
引用
@article{arxiv.2605.10422,
title = {On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields},
author = {A. V. Gorshkov},
journal= {arXiv preprint arXiv:2605.10422},
year = {2026}
}