Nonexistence of subcritical solitary waves

Vladimir Kozlov, Evgeniy Lokharu, Miles H. Wheeler

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/13923b61-35e3-40a1-8f16-fb4cebda48e0 • DOI: https://doi.org/10.1007/s00205-021-01659-y

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.

water waves solitary waves Water waves with vorticity /dk/atira/pure/subjectarea/asjc/2600/2603 name=Analysis /dk/atira/pure/subjectarea/asjc/2600/2601 name=Mathematics (miscellaneous) /dk/atira/pure/subjectarea/asjc/2200/2210 name=Mechanical Engineering