Nonexistence of Subcritical Solitary Waves

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Date
2020-03-15MFO Scientific Program
Research in Pairs 2019Series
Oberwolfach Preprints;2020,06Author
Kozlov, Vladimir
Lokharu, Evgeniy
Wheeler, Miles H.
Metadata
Show full item recordOWP-2020-06
Abstract
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.