Related papers: Low regularity solutions for gravity water waves I…
Regularizing effects of surface tension are studied for interfacial waves between a two-dimensional, infinitely-deep and irrotational flow of water and vacuum. The water wave problem under the influence of surface tension is formulated as a…
We prove via explicitly constructed initial data that solutions to the gravity-capillary wave system in $\mathbb{R}^3$ representing a 2d air-water interface immediately fails to be $C^3$ with respect to the initial data if the initial data…
We prove a long-term regularity result for three-dimensional gravity water waves with small initial data but nonzero initial vorticity. We consider solutions whose vorticity vanishes on the free boundary and use this to derive a system for…
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…
We consider the angle $\theta$ of inclination (with respect to the horizontal) of the profile of a steady 2D inviscid symmetric periodic or solitary water wave subject to gravity. Although $\theta$ may surpass 30$^\circ$ for some…
In this paper we construct periodic capillarity-gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by reexpressing, in the height function formulation of the water wave problem, the boundary condition…
We consider two-dimensional periodic gravity water waves with constant nonzero vorticity $\gamma$, in infinite depth and with periodic boundary conditions. We prove that, if the characteristic wave number $\frac{\gamma^2}{g}$ is rational,…
We consider the two dimensional gravity water wave equation in the regime that includes free surfaces with angled crests. We assume that the fluid is inviscid, incompressible and irrotational, the air density is zero, and we neglect the…
In this article we consider the low regularity well-posedness of the surface quasi-geostrophic (SQG) front equation. Recent work on other quasilinear models, including the gravity water waves system and nonlinear waves, have demonstrated…
This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of…
We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. This study focuses on domains with flat bottom topography and conditions ranging from deep to…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
As a starting point of studying the long time behavior of the $3D$ water waves system in the flat bottom setting, in this paper, we try to improve the understanding of the Dirichlet-Neumann operator in this setting. As an application, we…
In this work we discuss an approximate model for the propagation of deep irrotational water waves, specifically the model obtained by keeping only quadratic nonlinearities in the water waves system under the Zakharov/Craig-Sulem…
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 consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…
This paper is devoted to the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the general question of proving Morawetz inequalities. We continue the analysis initiated in our previous work, where we…
This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
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…