论文标题
具有一般涡度和临界层的大振幅稳定重力水波
Large-amplitude steady gravity water waves with general vorticity and critical layers
论文作者
论文摘要
我们考虑在有限深度的水上具有二维稳定的周期性重力波，并有规定但任意的涡度分布。允许水面悬垂，并且没有关于缺乏停滞点和临界层的假设。我们使用保形映射和对伯努利方程的新重新重新制定，我们将同等的表述视为“身份和紧凑型”，这是Rabinowitz的全球分叉定理。这使我们能够构建一组全球连接的溶液集，该解决方案是从层流的层流进行分叉的。此外，在涉及涡度函数的一定光谱假设下，对这些溶液进行了淋巴结分析。最后，更详细地研究了下游波。
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new reformulation of Bernoulli's equation, we uncover an equivalent formulation as "identity plus compact," which is amenable to Rabinowitz's global bifurcation theorem. This allows us to construct a global connected set of solutions, bifurcating from laminar flows with a flat surface. Moreover, a nodal analysis is carried out for these solutions under a certain spectral assumption involving the vorticity function. Lastly, downstream waves are investigated in more detail.
