相关论文: Two dimensional solitary water waves with constant…

This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency…

We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of…

We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…

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…

This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface…

We consider the two-dimensional capillary water waves with nonzero constant vorticity in infinite depth. We first derive the Babenko equation that describes the profile of the solitary wave. When the velocity $c$ is close to a critical…

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…

In this paper, we study two-dimensional traveling waves in finite-depth water that are acted upon solely by gravity. We prove that, for any supercritical Froude number (non-dimensionalized wave speed), there exists a continuous…

In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes…

For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our…

We prove the existence of pure capillary solitary waves for the 2D finite-depth Euler equations with nonzero constant vorticity. In the irrotational case, nonexistence of solitary waves was established by Ifrim--Pineau--Tataru--Taylor, so…

In this paper, we study solitary waves propagating along the surface of an infinitely deep body of water in two or three dimensions. The waves are acted upon by gravity and capillary effects are allowed --- but not required --- on the…

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

This article is concerned with the incompressible, infinite depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity…

We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless…

The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…

Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…

We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves…