In this paper, we consider the $3D$ water waves system above a fixed flatbottom (finite depth) with gravity, meanwhile without surface tension (thegravity water waves system). For this system, we prove global existence forsuitably small initial data and non-existence of traveling waves below acertain level of smallness, which strongly contrasts the behavior of thesolution of the same system in the $2D$ case.
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机译：在本文中，我们认为$ 3D $水波系统以重力的固定平板（有限深度）上方，同时没有表面张力（Thegravity水波系统）。对于该系统，我们证明了全球性存在性的初始数据，并且不存在旅行波的行驶波的不存在水平，这与2D $案例中相同系统的行为强烈造影。
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