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arXiv · 1503.00649

Representation of vector fields

A. G. Ramm
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Abstract

A simple proof is given for the explicit formula which allows one to recover a $C^2-$smooth vector field $A=A(x)$ in $\mathbb{R}^3$, decaying at infinity, from the knowledge of its $\nabla \times A$ and $\nabla \cdot A$. The representation of $A$ as a sum of the gradient field and a divergence-free vector fields is derived from this formula. Similar results are obtained for a vector field in a bounded $C^2-$smooth domain.

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A. G. Ramm. 2015-03-02. Representation of vector fields. https://arxiv.org/abs/1503.00649

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