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<p>We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are the first such results on an unbounded resp.&#xa0;any 2D domain.</p>

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Maximal double-exponential growth for the Euler equation on the half-plane

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Andrej Zlatoš

摘要

We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are the first such results on an unbounded resp. any 2D domain.