Related papers: Local smoothing effects for the water-wave problem…

This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…

Polymer brushes are increasingly used to tailor surface physicochemistry for various applications such as wetting, adhesion of biological objects, implantable devices, etc. We perform Dissipative Particle Dynamics simulations to study the…

We consider dissipation of surface waves on fluids, with a view to its effects on analogue gravity experiments. We begin by reviewing some general properties of wave dissipation, before restricting our attention to surface waves and the…

We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…

We study the surface tension of electrolyte solutions at the air/water and oil/water interfaces. Employing field-theoretical methods and considering short-range interactions of anions with the surface, we expand the Helmholtz free energy to…

This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density…

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It…

Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude capillary waves in the…

We prove a weighted a priori energy estimate for the two dimensional water-waves problem with contact points in the absence of gravity and surface tension. When the surface graph function and its time derivative have some decay near the…

We prove the local existence for the Water Waves equations with large bathymetric variations on a time interval of size 1/\epsilon, where $\epsilon$ measures the amplitude of the wave. We just need the presence of surface tension.

Surface tension has a strong influence on the shape of fluid interfaces. We propose a method to calculate the corresponding forces efficiently. In contrast to several previous approaches, we discriminate to this end between surface and…

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.

In this work, we propose and compare three numerical methods to handle the one-phase Hele-Shaw problem with surface tension in dimension two by using three variational approaches in the spirit of the seminal works \cite{Otto, Gia_Otto}.

We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

This paper is devoted to the 2D gravity-capillary water waves equations in their Hamiltonian formulation, addressing the general question of proving Morawetz inequalities. We continue the analysis initiated in our previous work, where we…

We propose higher-order approximation formulae recovering the surface elevation from the pressure at the bed and the background shear flow for small-amplitude Stokes and solitary water waves. They offer improvements over the pressure…

This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We…

A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with…