相关论文: No pure capillary solitary waves exist in 2D finit…

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 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…

The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water, under the influence of gravity, is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to…

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…

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…

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 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…

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…

The paper deals with the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the question of the nonlinear interaction of a plane wave with its reflection off a vertical wall. The main result is the…

In this paper, we prove global regularity, scattering, and the non-existence of small traveling waves for the $3D$ finite depth capillary waves system for small initial data. The non-existence of small traveling waves shows a fundamental…

In this paper we prove a global regularity result for a quadratic quasilinear model associated to the water waves system with surface tension and no gravity in dimension two (the capillary waves system). The model we consider here retains…

The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…

This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential…

We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…

Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions…

This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a…

Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e. sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The…

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…

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…