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<p>In this paper, we study the Cauchy problem for a Benjamin-Ono type equation. We first establish a local well-posedness result and then prove that, for some initial data, solutions exist for all time, while for other initial data, blow-up occurs in finite time.</p>

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A note on a Benjamin-Ono type equation

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Zhen Yuan,
  • Feiyao Ma,
  • Weifeng Wo

摘要

In this paper, we study the Cauchy problem for a Benjamin-Ono type equation. We first establish a local well-posedness result and then prove that, for some initial data, solutions exist for all time, while for other initial data, blow-up occurs in finite time.