论文标题
亚临界孤独波不存在
Nonexistence of subcritical solitary waves
论文作者
论文摘要
我们证明，具有亚临界波速度和任意涡度分布的二维孤立重力水波不存在。这是一个长期以来的开放问题，即使在无关的情况下，也只有部分依赖于标志条件或较小的假设。作为推论，我们获得了相对完整的孤立波的分类：它们必须是超临界，对称的，并且在中央波峰的任何一侧都必须单调减少。该证明引入了与所谓的流动力相关的新功能，并具有多种令人惊讶的属性。除了孤立波外，我们的不存在的结果适用于仅在一个方向上衰减的“半生态”波（例如孔）。
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to "half-solitary" waves (e.g. bores) which decay in only one direction.
