Related papers: Decay of viscous surface waves without surface ten…
In this paper, we present a new framework for the global well-posedness and large-time behavior of a two-phase flow system, which consists of the pressureless Euler equations and incompressible Navier-Stokes equations coupled through the…
This paper explores decaying turbulence beneath surface waves that is initially isotropic and shear-free. We start by presenting phenomenology revealed by wave-averaged numerical simulations: an accumulation of angular momentum in coherent…
We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the boundary…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still…
The energy of solutions of the scalar damped wave equation decays uniformly exponentially fast when the geometric control condition is satisfied. A theorem of Lebeau [leb93] gives an expression of this exponential decay rate in terms of the…
We show that there exists an exact solution for a lossless and reciprocal periodic surface impedance which ensures full conversion of a single-mode surface wave propagating along the impedance boundary to a single plane wave propagating…
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical…
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…
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential velocity at the…
We report on the observation of freely decaying capillary wave turbulence on the surface of a fluid. The capillary wave turbulence spectrum decay is found to be self-similar in time with the same power law exponent than the one found in the…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
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…
In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by boundary-fitted unstructured meshes, or, where possible, by mapping the complex…
We develop the asymptotic behavior for the solutions to the stationary Navier-Stokes equation in the exterior domain of the 2D hyperbolic space. More precisely, given the finite Dirichlet norm of the velocity, we show the velocity decays to…
It is known that an axisymmetric viscous film flowing down the outside of a thin vertical fiber becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions and…
We present a novel approach to the analysis of regularity and decay for solutions of wave equations in a neighborhood of null infinity in asymptotically flat spacetimes of any dimension. The classes of metrics and wave type operators we…
Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…
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…