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We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…

Analysis of PDEs · Mathematics 2016-02-02 Ioannis Giannoulis

We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable…

Analysis of PDEs · Mathematics 2025-03-31 Qingtang Su , Siwei Wang

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…

Analysis of PDEs · Mathematics 2017-02-28 Massimiliano Berti , Jean-Marc Delort

Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…

Fluid Dynamics · Physics 2022-07-01 D. Tseluiko , N. S. Alharthi , R. Barros , K. R. Khusnutdinova

This paper is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover,…

Analysis of PDEs · Mathematics 2014-04-17 Thomas Alazard , Nicolas Burq , Claude Zuily

We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…

Classical Physics · Physics 2020-04-06 Mohamed Farhat , Pai-Yen Chen , Hakan Bagci , Khaled Salama , Sebastien Guenneau

The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…

Analysis of PDEs · Mathematics 2021-01-13 Evgueni Dinvay , Dag Nilsson

We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…

General Relativity and Quantum Cosmology · Physics 2011-11-28 Maarten van de Meent

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

This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is…

Analysis of PDEs · Mathematics 2015-08-11 Santosh Bhattarai

We are concerned with the stability of thin liquid films overflowing single microstructures with sharp corners. The microstructures were of rectangular and triangular shape. Their heights and widths were 0.25, 0.5 and 0.75 times the Nusselt…

Fluid Dynamics · Physics 2020-09-09 Henning Bonart , Johannes Jung , Jens-Uwe Repke

This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general…

Analysis of PDEs · Mathematics 2018-05-09 Mark Groves , Dag Nilsson

The two dimensional gravity water wave problem concerns the motion of an incompressible fluid occupying half the 2D space and flowing under its own gravity. In this paper we study long-term regularity of solutions evolving from small but…

Analysis of PDEs · Mathematics 2022-06-22 Fan Zheng

We discuss axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal…

Analysis of PDEs · Mathematics 2025-11-13 Mark D. Groves , Dag Nilsson , Leon Schütz

Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…

Fluid Dynamics · Physics 2025-02-26 Alex Doak , Vera Mikyoung Hur , Jean-Marc Vanden-Broeck

Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…

Atmospheric and Oceanic Physics · Physics 2014-06-09 I. M. Mindlin

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…

Fluid Dynamics · Physics 2020-01-29 Vasyl P. Lukomsky , Ivan S. Gandzha

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…

General Relativity and Quantum Cosmology · Physics 2007-05-23 J. C. Fabris , S. V. B. Goncalves

Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an…

General Relativity and Quantum Cosmology · Physics 2024-09-26 Alessia Biondi , Scott Robertson , Germain Rousseaux

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