We present the almost global in time existence result in [13] of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity and we describe the ideas of proof. This is based on a novel Hamiltonian paradifferential Birkhoff normal form approach for quasi-linear PDEs.

中文翻译：

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水波的哈密顿准微分 Birkhoff 范式

我们在[13]中提出了具有恒定涡量的一维重力-毛细管水波方程的小振幅空间周期解的几乎全局时间存在性结果，并描述了证明的思想。这是基于准线性偏微分方程的新型哈密顿准微分 Birkhoff 范式方法。