English
Related papers

Related papers: Steady periodic gravity waves with surface tension

200 papers

This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water either in a flow of finite depth and constant vorticity over an impermeable flat bed or in an irrotational flow of great…

Analysis of PDEs · Mathematics 2014-04-25 Peter de Boeck

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…

Analysis of PDEs · Mathematics 2015-06-12 Jalal Shatah , Samuel Walsh , Chongchun Zeng

In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…

Analysis of PDEs · Mathematics 2026-03-24 Jifeng Chu , Zihao Wang , Yong Zhang

We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…

Analysis of PDEs · Mathematics 2025-08-19 Benjamin F. Akers , David M. Ambrose , Davia W. Sulon

This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water…

Analysis of PDEs · Mathematics 2021-07-30 Robin Ming Chen , Samuel Walsh , Miles H. Wheeler

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Analysis of PDEs · Mathematics 2025-06-23 Alex Doak , Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

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…

Analysis of PDEs · Mathematics 2021-03-17 Massimiliano Berti , Luca Franzoi , Alberto Maspero

We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…

Analysis of PDEs · Mathematics 2020-06-18 Mats Ehrnström , Samuel Walsh , Chongchun Zeng

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…

Analysis of PDEs · Mathematics 2007-11-28 Vera Mikyoung Hur , Zhiwu Lin

This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…

Analysis of PDEs · Mathematics 2025-08-07 Yong Zhang

By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…

Analysis of PDEs · Mathematics 2024-01-23 Ola Mæhlen , Douglas Svensson Seth

We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhanging, including one which intersects itself to enclose a…

Analysis of PDEs · Mathematics 2022-05-24 Vera Mikyoung Hur , Miles H. Wheeler

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…

Analysis of PDEs · Mathematics 2008-05-06 Pietro Baldi , John F. Toland

This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…

Analysis of PDEs · Mathematics 2025-09-22 Liang Li , Quan Wang

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…

Analysis of PDEs · Mathematics 2015-06-18 Anca-Voichita matioc , Bogdan-Vasile Matioc

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…

Analysis of PDEs · Mathematics 2022-09-13 Junichi Koganemaru , Ian Tice

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…

Analysis of PDEs · Mathematics 2009-12-02 Vera Mikyoung Hur

We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…

Analysis of PDEs · Mathematics 2021-11-01 Roberto Feola , Filippo Giuliani

We study the transverse dynamics of two-dimensional traveling periodic waves for the gravity--capillary water-wave problem. The governing equations are the Euler equations for the irrotational flow of an inviscid fluid layer with free…

Analysis of PDEs · Mathematics 2022-03-29 Mariana Haragus , Tien Truong , Erik Wahlén

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

Analysis of PDEs · Mathematics 2026-04-28 Tingting Feng , Yong Zhang , Zhitao Zhang