Related papers: A remark on the two dimensional water wave problem…
By using a limit analysis for the motion equations of viscous fluid endowed with internal capillarity, we are able to propose a dynamical expression for the surface tension of moving liquid-vapour interfaces without any phenomenological…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
The long-range contribution to dispersion forces is known to have a major impact on the properties of inhomogeneous fluids, and its correct treatment is increasingly recognized as being a necessary requirement to avoid cutoff-related…
The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillation. There exists a simple…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
This article is concerned with the incompressible, infinite depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…
With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative…
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
This work addresses four problems in defining and computing the surface tension of vapour-liquid interfaces: (1) The apparent kinetic contribution to the surface tension, and what it is that makes it appear; (2) the problem of defining the…
An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive…
A class of water wave problems concerns the dynamics of the free interface separating an inviscid, incompressible and irrotational fluid, under the influence of gravity, from a zero-density region. In this note, we present some recent…
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…
Roughening of interfaces implies the divergence of the interface width $w$ with the system size $L$. For two-dimensional systems the divergence of $w^2$ is linear in $L$. In the framework of a detailed capillary wave approximation and of…
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity.…
In this study we try to answer the qustion : What happens when explicit constraints are introduced such that the low energy, long wavelength modes of a system are unavailable ? This question has assumed some importance in recent years due…
Based on the a priori estimates in our previous work \cite{MW}, we continue to investigate the water-waves problem in a bounded two dimensional corner domain in this paper. We prove the local well-posedness of the solution to the…
We present here a survey of recent results concerning the mathematical analysis of instabilities of the interface between two incompressible, non viscous, fluids of constant density and vorticity concentrated on the interface. This…