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.

我们证明了不存在具有亚临界波速和任意涡度分布的二维孤立重力水波。这是一个长期存在的开放问题，即使在非旋转情况下，也只有部分结果取决于符号条件或较小的假设。作为推论，我们获得了一个相对完整的孤立波分类：它们必须是超临界的，对称的并且在中心波峰的两侧单调递减。该证明引入了一个新功能，该功能与所谓的流动力有关，并具有一些令人惊讶的特性。除了孤立波，我们的不存在结果适用于仅在一个方向上衰减的“半孤立”波（例如孔）。