Related papers: A remark on the two dimensional water wave problem…
We consider the wave equation $\varepsilon^2(-\partial_t^2 + \Delta)u + f(u) = 0$ for $0<\varepsilon\ll 1$, where $f$ is the derivative of a balanced, double-well potential, the model case being $f(u) = u-u^3$. For equations of this form,…
Using fluorescence microscopy we study the adsorption of single latex microparticles at a water/water interface between demixing aqueous solutions of polymers, generally known as a water-in-water emulsion. Similar microparticles at the…
In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…
This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the…
The Muskat problem, in its general setting, concerns the interface evolution between two incompressible fluids of different densities and viscosities in porous media. The interface motion is driven by gravity and capillarity forces, where…
We examine a two-media 2-dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface with wind generated surface waves but considered bounded above by a lid by an assumption…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…
Due to the simultaneous presence of bulk-like and interfacial fluctuations the understanding of the structure of liquid-vapour interfaces poses a long-lasting and ongoing challenge for experiments, theory, and simulations. We provide a new…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
We study both diffuse and sharp liquid-vapor interfaces. The equilibrium equation of fluids is derived by using the principle of virtual work in a domain including the interfaces. For diffuse interfaces, the surface tension coefficient…
A version of model is proposed, which is aimed for getting parameters of the atmospheric layer and upper water layer with account of the wind-wave state. The dynamics of the atmospheric boundary layer is realized in version of papers [1,…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…
A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the…
Vibrations can dynamically stabilize otherwise unstable liquid interfaces and produce new dynamic equilibria, called vibro-equilibria. Typically, the vibrations are homogeneous in the liquid and the liquid interface remains approximately…
We consider the one-dimensional shallow water problem with capillary surfaces and moving contact {lines}. An energy-based model is derived from the two-dimensional water wave equations, where we explicitly discuss the case of a stationary…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is…