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<p>We study the Cauchy problem for a nonlocal evolution model arising in equatorial ocean flows. We prove global existence of solutions for small initial data in critical Besov spaces and show that these solutions become instantly spatially analytic. Our approach introduces exponentially weighted unknowns to capture the interplay between the dissipative linear operator and the nonlocal Hilbert transform, allowing precise control of the bilinear nonlinearity. This provides a unified framework to extend small-data global existence and analyticity results from classical fluid equations to a nonlocal dispersive-dissipative setting.</p>

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Global Existence and Analyticity of the Equatorial Ocean Flow Model in Critical Besov Spaces

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Bingbing Dai,
  • Zhen He,
  • Wei Luo,
  • Zhaoyang Yin

摘要

We study the Cauchy problem for a nonlocal evolution model arising in equatorial ocean flows. We prove global existence of solutions for small initial data in critical Besov spaces and show that these solutions become instantly spatially analytic. Our approach introduces exponentially weighted unknowns to capture the interplay between the dissipative linear operator and the nonlocal Hilbert transform, allowing precise control of the bilinear nonlinearity. This provides a unified framework to extend small-data global existence and analyticity results from classical fluid equations to a nonlocal dispersive-dissipative setting.