On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields

A. V. Gorshkov

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arXiv · 2605.10422

On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields

A. V. Gorshkov

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Abstract

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.

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A. V. Gorshkov. 2026-05-11. On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields. https://arxiv.org/abs/2605.10422

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