Related papers: A priori estimates for water waves with emerging b…
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…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the ``frozen'' sea bed deformation to the…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
The base of a jet impinging on an ultrapure water bath is studied experimentally. At the impact point, a train of capillary waves develops along the jet. By performing Particle Tracking Velocity measurements, we show that there is a…
An adjoint based technique is applied to a shallow water model in order to estimate the influence of the model's parameters on the solution. Among parameters the bottom topography, initial conditions, boundary conditions on rigid…
In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water)…
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…
General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are…
We consider an incompressible viscous flow without surface tension in a finite- depth domain of three dimension, with free top boundary. This system is governed by a Naiver-Stokes equation in a moving domain and a transport equation for the…
In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
Wetting is a widespread phenomenon, most prominent in a number of cases, both in nature and technology. Droplets of pure water with initial radius ranging from 20 to 80 [\AA] spreading on graphitic surfaces are studied by molecular dynamics…
We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of…
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…
In this paper, the phenomenon of band gaps and Anderson localization of water waves over one-dimensional periodic and random bottoms is investigated by the transfer matrix method. The results indicate that the range of localization in…
We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a…
Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…
Analysing the impact of bottom friction on shallow water waves over bottom terrains is important in areas including environmental and coastal engineering as well as the oceanic and atmospheric sciences. However, current theoretical…