On the existence theory for irrotational water waves
On the existence theory for irrotational water waves
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DOI：
10.1017/s0305004100054372
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发表时间：
1978-01
影响因子：
0.8
通讯作者：
G. Keady;J. Norbury
中科院分区：
文献类型：
--
作者：
G. Keady;J. Norbury
摘要本文研究了理想液体在水平面上流动时，其表面的定常平面周期波。气流是无旋的。体积流量用Q表示，速度势用ø表示，波的周期用2L表示，表面切线与水平面的最大倾角θm表示。Krasovskii（12）建立了在每个固定的Q和L处，θm的每个值严格在0到1 / 6 π之间存在波解。我们建立了在每一个固定的Q和L处，严格在c和0之间，qc的每一个值都存在波解。这里qc是峰值处的流速，g是重力加速度。Krasovskii的解集包含在我们得到的集合中。
Abstract This paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by ø, the period in ø of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm. Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, and where g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.