Related papers: A remark on the two dimensional water wave problem…
We consider the two-dimensional water wave problem in the case where the free interface of the fluid meets a vertical wall at a possibly non-right angle; and where the free interface can be non-$C^1$ with angled crests. We assume that the…
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 study the two dimensional water waves problem with surface tension in the case when there is a non-zero contact angle between the free surface and the bottom. In the presence of surface tension, dissipations take place at the contact…
We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and…
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…
In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…
We consider a coupled system of partial differential equations describing the interactions between a closed free interface and two viscous incompressible fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes equations…
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…
We consider the two-dimensional water wave problem in an infinitely long canal of finite depth both with and without surface tension. In order to describe the evolution of the envelopes of small oscillating wave packet-like solutions to…
A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…
We consider the dynamics of a layer of an incompressible electrically conducting fluid interacting with the magnetic field in a two-dimensional horizontally periodic setting. The upper boundary is in contact with the atmosphere, and the…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
The equation of motions and the conditions on surfaces and edges between fluids and solids in presence of non-constant surface energies, as in the case of surfactants attached to the fluid particles at the interfaces, are revisited under…
This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface…
In this paper we develop an existence theory for small amplitude, steady, two-dimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin--Helmholtz type discontinuity across the…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal…
Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at…