Related papers: A Weak Formulation of Water Waves in Surface Varia…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic…
We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques,…
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.
We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…
We address ring-shaped surface waves supported by defocusing thermal media with circular cross-section. Such waves exist because of the balance between repulsion from the interface and deflection of light from the bulk medium due to…
This paper presents the second-order perturbation theory of the Navier-Stokes equations for free surface flows, with the wave amplitude considered as the perturbation parameter. Gravity-capillary surface waves in incompressible viscous…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-Holm equation by a variational approach in the Lagrangian formalism.
In the present study a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth's rotation is derived by following the formal asymptotic procedures. Such a model equation is analogous to…
In this paper, we study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. We adopt the frequency domain method to prove that the system with smooth initial data is…
Hammack & Segur (1978) conducted a series of surface water-wave experiments in which the evolution of long waves of depression was measured and studied. This present work compares time series from these experiments with predictions from…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
We study traveling waves for a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions. We describe relations between speeds and asymptotic of profiles of…