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In these notes, we consider a two-dimensional model of a nonlinear dispersive equation originated in gravity-capillary waves. Our objective is to establish that the solutions of this model have a local gain of half-derivative in the first variable in both real and cylinder settings. We use energy estimates that depend on various commutator estimates for non-local operators to obtain our results.

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A Note on Kato’s Smoothing Effect for a Dispersive Model Arising in Capillary-Gravity Flows

  • 会议论文

  • 发表日期：

    2026年

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  • Carlos Garzón,
  • Oscar Riaño

摘要

In these notes, we consider a two-dimensional model of a nonlinear dispersive equation originated in gravity-capillary waves. Our objective is to establish that the solutions of this model have a local gain of half-derivative in the first variable in both real and cylinder settings. We use energy estimates that depend on various commutator estimates for non-local operators to obtain our results.