Representation of vector fields
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<p>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.</p>
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2007 ◽
Vol 27
(5)
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pp. 1399-1417
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2018 ◽
Vol 148
(4)
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pp. 773-818
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2014 ◽
Vol 24
(07)
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pp. 1450090
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2021 ◽
Vol 373
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pp. 113574
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