Influence of bottom topography on long water waves
Influence of bottom topography on long water waves
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DOI：
10.1051/m2an:2007041
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发表时间：
2007-01
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影响因子：
--
通讯作者：
F. Chazel
中科院分区：
文献类型：
--
作者：
F. Chazel
在这里，我们专注于水波问题不均匀的底部在长波制度，在一个无界的二维或三维域。为了推导出该问题的渐进模型，我们考虑了两种不同的底部地形状态，一种用于振幅的小变化，另一种用于振幅的强变化。从该问题的Zakharov公式出发，严格计算了所涉及的Dirichlet-Neumann算子的渐近展开式。然后，根据Bona，Colin和Lannes提出的全局策略，导出了适用于各种海底地形的新的对称渐近模型。这些系统的解决方案被证明给水波问题的解决方案很好的近似。这些结果适用于在无穷远处消失的解以及空间周期解。
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotics expansion of the involved Dirichlet-Neumann operator. then, following the global strategy introduced by Bona, Colin and Lannes, new symetric asymptotic models are derived for each regime of bottom topography. Solutions of these systems are proved to give good approximations of solutions of the water waves problem. These results hold for solutions that evanesce at infinity as well as for spatially periodic ones.