Related papers: On the gravity-capillary water waves with point vo…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We establish the existence of gravity water waves by applying a mountain pass theorem to a singular perturbation of the Alt-Caffarelli functional associated with the two-dimensional water wave equations. Our approach is formulated entirely…
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic…
In this experimental study, we investigate the interaction of gravity-capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source…
The last decade has seen a significant increase in the number of studies devoted to wave turbulence. Many deal with water waves, as modeling of ocean waves has historically motivated the development of weak turbulence theory, which adresses…
We study the tensorial modes of the two-fluid model, where one of this fluids has an equation of state $p = - \rho/3$ (variable cosmological constant, cosmic string fluid, texture) or $p = - \rho$ (cosmological constant), while the other…
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…
We prove the existence and the linear stability of small amplitude time {\it quasi-periodic} standing wave solutions (i.e. periodic and even in the space variable $ x $) of a $ 2 $-dimensional ocean with infinite depth under the action of…
We prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a…
Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical…
We consider the Cauchy problem for the 2D gravity water wave equation. Recently Wu \cite{Wu15, Wu18} proved the local well-posedness of the equation in a regime which allows interfaces with angled crests as initial data. In this work we…
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 study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy…
This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. We prove that the Cauchy problem in Sobolev spaces is uniquely solvable for data $\frac{1}{4}$ derivatives less…
We consider the 2D gravity water waves equation on an infinite domain. We prove a local wellposedness result which allows interfaces with corners and cusps as initial data and which is such that the time of existence of solutions is uniform…
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under…
This paper presents the second-order perturbation theory of the Navier-Stokes equations for free surface flows, with the wave amplitude considered as the perturbation parameter. Gravity-capillary surface waves in incompressible viscous…
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
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…