论文标题
全球分叉和有限深度水上的最高波
Global bifurcation and highest waves on water of finite depth
论文作者
论文摘要
我们认为在有限深度的水上具有涡度的稳定水波的二维问题。在忽略表面张力的效果的同时，我们构建了接近极限波的大幅度周期波的家族，这要么是孤立波，最高的孤立波，最高的stokes波，还是具有破坏性轮廓的Stokes Wave。特别是，当涡度不负时，我们证明存在最高的stokes波，其中包含的角度为120度。与以前的研究相反，我们将Bernoulli常数固定，并将波长视为分叉参数，从而确保极限波具有有限的深度。实际上，这是在有限深度的水上存在极端stokes波的第一个严格证明。除了最高波的存在之外，我们还为Stokes Wave的任意振幅的规律性（包括极端波）提供了新的结果。此外，我们证明了有关稳定波的几个新事实，例如在斯托克斯波的波长的下界，同时也消除了波浪破裂的可能性，即具有非负涡度的波浪。
We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching the limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120 degrees. In contrast to previous studies we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Beside the existence of highest waves we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminate a possibility of the wave breaking for waves with non-negative vorticity.
