Related papers: Finite depth gravity water waves in holomorphic co…
We consider the gravity water waves system in the case of a one dimensional interface, for sufficiently smooth and localized initial data, and prove global existence of small solutions. This improves the almost global existence result of Wu…
The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV…
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such…
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…
We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.
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…
This paper addresses deep-water gravity waves of finite amplitude generated by an initial disturbance to the water. It is assumed that the horizontal dimensions of the initially disturbed body of the water are much larger than the magnitude…
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 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…
In this paper, we consider 2D incompressible Euler equations in an unbounded domain with a free surface and a fixed bottom at finite depth. The fluid motion is under the influence of gravity and surface tension. We construct initial data…
We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and…
We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…
Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…
In this paper, we prove the existence of two-dimensional, traveling, capillary-gravity, water waves with compactly supported vorticity. Specifically, we consider the cases where the vorticity is a $\delta$-function (a point vortex), or has…
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled…
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.
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
The stability of binary orbits can significantly shape the gravity wave signal which future Earth-based interferometers hope to detect. The inner most stable circular orbit has been of interest as it marks the transition from the late…
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size $\epsilon$, is almost…
The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically…