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<p>We consider axisymmetric, swirl-free solutions of the Euler equations in three and higher dimensions, of generalized anti-parallel-vortex-tube-pair-type: the initial scalar vorticity has a sign in the half-space, is odd under reflection across the plane, is bounded and decays sufficiently rapidly at the axis and at spatial infinity. We prove lower bounds on the growth of such solutions in all dimensions. In particular in three dimensions, we improve a recent lower bound of Choi and Jeong&#xa0;[<CitationRef CitationID="CR5">5</CitationRef>].</p>

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Growth Rates for Anti-Parallel Vortex Tube Euler Flows in Three and Higher Dimensions

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Stephen Gustafson,
  • Evan Miller,
  • Tai-Peng Tsai

摘要

We consider axisymmetric, swirl-free solutions of the Euler equations in three and higher dimensions, of generalized anti-parallel-vortex-tube-pair-type: the initial scalar vorticity has a sign in the half-space, is odd under reflection across the plane, is bounded and decays sufficiently rapidly at the axis and at spatial infinity. We prove lower bounds on the growth of such solutions in all dimensions. In particular in three dimensions, we improve a recent lower bound of Choi and Jeong [5].