Related papers: On the capillary water waves with constant vortici…

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…

The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for the well-posedness of this system requires initial velocity…

A nonlinear Schr\"odinger equation for the envelope of two-dimensional gravity-capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity-capillary…

We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary…

We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…

Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…

This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…

In this article, we develop the local Cauchy theory for the gravity water waves system, for rough initial data which do not decay at infinity. We work in the context of $L^2$-based uniformly local Sobolev spaces introduced by Kato. We prove…

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…

Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…

We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform…

This paper is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover,…

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…

This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We…

We provide the first proof of local well-posedness for the two-dimensional gravity water wave equations with spatially quasi-periodic initial conditions. We represent the solution using holomorphic coordinates, which are equivalent to a…

We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general…

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…

In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…

We construct small amplitude gravity-capillary water waves with small nonzero vorticity, in three spatial dimensions, bifurcating from uniform flows. The waves are symmetric, and periodic in both horizontal coordinates. The proof is…

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…