Related papers: The Benjamin-Ono approximation for 2D gravity wate…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
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…
The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity…
The Okubo [2]-Weiss [3] criterion is recast by using the 2D hydrodynamic Beltrami condition (Shivamoggi et al.[13]) that approximates the slow flow-variation ansatz imposed in its derivation. This turns out to provide an interesting…
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…
A new type of steady steep two-dimensional irrotational symmetric periodic gravity waves on inviscid incompressible fluid of infinite depth is revealed. We demonstrate that these waves have sharper crests in comparison with the Stokes waves…
In this paper we consider three-dimensional steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are…
We study a fundamental model in fluid mechanics--the 3D gravity water wave equation, in which an incompressible fluid occupying half the 3D space flows under its own gravity. In this paper we show long-term regularity of solutions whose…
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…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
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…
We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity…
We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching the…
Considered here are two systems of equations modeling the two-way propagation of long-crested, long-wavelength internal waves along the interface of a two-layer system of fluids in the Benjamin-Ono and the Intermediate Long-Wave regime,…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
This article concerns the water wave problem in a three-dimensional domain of infinite depth and examines the modulational regime for weakly nonlinear wavetrains. We use the method of normal form transformations near the equilibrium state…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…
In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…