Related papers: Finite depth gravity water waves in holomorphic co…
We study non-scattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at most finitely many wave numbers such that Herglotz incident…
This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…
The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We prove an almost global in time existence result of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity. The result holds for any value of gravity, vorticity and depth and any…
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth, and prove a rigorous reduction of these equations to Birkhoff normal form up to degree four. This proves a conjecture of…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…
The gravity water waves equations describe the evolution of the surface of an incompressible, irrotational fluid in the presence of gravity. The classical regularity threshold for the well-posedness of this system requires initial velocity…
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…
Propagation of weak gravitational waves, when a dynamical four-form is around, has been investigated. Exact, self-consistent solutions corresponding to plane, monochromatic gravitational waves have been studied.
The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is investigated. Some new results on the generation of gravity-capillary waves are presented which supplement the…
Gravitational waves with parallel rays are known to have remarkable properties: Their orbit space of null rays possesses the structure of a non-relativistic spacetime of codimension-one. Their geodesics are in one-to-one correspondence with…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…
The aim of this paper is to prove the existence of gravity-capillary Crapper waves with the presence of vorticity. In particular, we consider a concentrated vorticity: point vortex and vortex patch. We show that for small gravity and small…
We establish a generic, fully-relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically-symmetric, non-vacuum black-hole spacetimes. The potential applications to astrophysical setups range…
We prove an extended lifespan result for the full gravity-capillary water waves system with a $2$ dimensional periodic interface: for initial data of sufficiently small size $\varepsilon$, smooth solutions exist up to times of the order of…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…