Solitary waves on rotational flows with an interior stagnation point
Mathematical Physics
2020-10-28 v3 Analysis of PDEs
math.MP
Abstract
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we construct a solution with the following properties. The corresponding flow is unidirectional at infinity and has a solitary wave of elevation as its upper boundary; under this unidirectional flow, there is a bounded domain adjacent to the bottom, which surrounds an interior stagnation point and is divided into two subdomains with opposite directions of flow by a critical level curve connecting two stagnation points on the bottom.
Keywords
Cite
@article{arxiv.1904.00401,
title = {Solitary waves on rotational flows with an interior stagnation point},
author = {Vladimir Kozlov and Nikolai G. Kuznetsov and Evgeniy Lokharu},
journal= {arXiv preprint arXiv:1904.00401},
year = {2020}
}