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<p>In this paper, we investigate Liouville type theorems for weak Beltrami flows and Beltrami flows with boundary. We obtain a mean value property and a monotonicity formula in a more general form, leading to a Liouville type theorem for weak Beltrami flows under five equivalent conditions. Furthermore, we demonstrate the continuity of the spherical integrals for Beltrami flows and establish Liouville type theorems for Beltrami flows with boundary.</p>

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Liouville Type Theorems for Beltrami Flows: Revisited

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Zengyun Qin,
  • Zhibing Zhang,
  • Qian Zu

摘要

In this paper, we investigate Liouville type theorems for weak Beltrami flows and Beltrami flows with boundary. We obtain a mean value property and a monotonicity formula in a more general form, leading to a Liouville type theorem for weak Beltrami flows under five equivalent conditions. Furthermore, we demonstrate the continuity of the spherical integrals for Beltrami flows and establish Liouville type theorems for Beltrami flows with boundary.