Remarks on a Liouville-type theorem for Beltrami flows

Dongho Chae; Peter Constantin

doi:10.1093/imrn/rnu233

Remarks on a Liouville-type theorem for Beltrami flows

Dongho Chae, Peter Constantin

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We present a simple, short, and elementary proof that if ν is a Beltrami flow with a finite energy in ℝ³, then ν =0. In the case of the Beltrami flows satisfying ν ∈ L _loc^∞ (ℝ³) ∩ L^q(ℝ³) with q ∈ [2, 3), or |ν(x)| = O(1/|x|^1+ε) for some ε >0, we provide a different, simple proof that ν =0.

Original language	English (US)
Pages (from-to)	10012-10016
Number of pages	5
Journal	International Mathematics Research Notices
Volume	2015
Issue number	20
DOIs	https://doi.org/10.1093/imrn/rnu233
State	Published - 2015

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1093/imrn/rnu233

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abstract = "We present a simple, short, and elementary proof that if ν is a Beltrami flow with a finite energy in ℝ3, then ν =0. In the case of the Beltrami flows satisfying ν ∈ L loc∞ (ℝ3) ∩ Lq(ℝ3) with q ∈ [2, 3), or |ν(x)| = O(1/|x|1+ε) for some ε >0, we provide a different, simple proof that ν =0.",

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AB - We present a simple, short, and elementary proof that if ν is a Beltrami flow with a finite energy in ℝ3, then ν =0. In the case of the Beltrami flows satisfying ν ∈ L loc∞ (ℝ3) ∩ Lq(ℝ3) with q ∈ [2, 3), or |ν(x)| = O(1/|x|1+ε) for some ε >0, we provide a different, simple proof that ν =0.

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Remarks on a Liouville-type theorem for Beltrami flows

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