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arXiv · 1904.01338

Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl

Naoki Hamamoto·Futoshi Takahashi
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Abstract

In this paper, we prove Hardy-Leray inequality for three-dimensional solenoidal (i.e., divergence-free) fields with the best constant. To derive the best constant, we impose the axisymmetric condition only on the swirl components. This partially complements the former work by O. Costin and V. Maz'ya \cite{Costin-Mazya} on the sharp Hardy-Leray inequality for axisymmetric divergence-free fields.

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Naoki Hamamoto, Futoshi Takahashi. 2019-04-02. Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl. https://arxiv.org/abs/1904.01338

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