Non-existence of three-dimensional travelling water waves with constant non-zero vorticity
Non-existence of three-dimensional travelling water waves with constant non-zero vorticity
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DOI：
10.1017/jfm.2014.131
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发表时间：
2014-04
影响因子：
3.7
通讯作者：
E. Wahlén
中科院分区：
文献类型：
--
作者：
E. Wahlén
摘要证明了在有限深度的水中不存在具有恒定非零涡度的三维有界重力波。在一定的表面压力条件下，当重力-毛细波足够小时，结果也成立。该证明依赖于椭圆方程的唯一延拓论证和liouville型结果。
Abstract We prove that there are no three-dimensional bounded travelling gravity waves with constant non-zero vorticity on water of finite depth. The result also holds for gravity–capillary waves under a certain condition on the pressure at the surface, which is satisfied by sufficiently small waves. The proof relies on unique continuation arguments and Liouville-type results for elliptic equations.