Related papers: 2D internal waves in an ergodic setting
In this note, we discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-known ellipticity of the energetic boundary integral formulation…
Petviashvili's method has been successfully used for approximating of solitary waves in nonlinear evolution equations. It was discovered empirically that the method may fail for approximating of periodic waves. We consider the case study of…
We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency,…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
We obtain weighted $L^2$ estimates for the elastic wave equation perturbed by singular potentials including the inverse-square potential. We then deduce the Strichartz estimates under the sole ellipticity condition for the Lam\'e operator…
Dynamics of the Fermi-Pasta-Ulam (FPU) system on a two-dimensional square lattice is considered in the limit of small-amplitude long-scale waves with slow transverse modulations. In the absence of transverse modulations, dynamics of such…
We show convergence of minimizers of weighted inertia-energy functionals to solutions of initial value problems for a class of nonlinear wave equations. The result is given for the nonhomogeneous case under a natural growth assumption on…
The vibration of a solid elastic cylinder is one of the classical applied problems of elastodynamics. Many fundamental forced-vibration problems involving solid elastic cylinders have not yet been studied or solved using the full…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform.…
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…
This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…
This paper is concerned with the asymptotic behavior of solutions of the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. We first introduce a continuous…
We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…
We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal…
In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make…
The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying…