Related papers: Finite depth gravity water waves in holomorphic co…
We have previously discussed the characteristics of the gravitational waves (GW) and have, theoretically, shown that, like the corresponding electromagnetic (EM) waves, they also demonstrate, under certain conditions, holographic…
We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…
We establish the existence of gravity water waves by applying a mountain pass theorem to a singular perturbation of the Alt-Caffarelli functional associated with the two-dimensional water wave equations. Our approach is formulated entirely…
Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical…
We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, two-dimensional sets of waves with several crests and troughs in…
We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating…
In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming these coefficients to vary with fluid density $\rho$ as $\rho^\lambda$, with $\lambda=1/2$…
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and subharmonic perturbations is calculated for each solution,…
We consider holography of two pp-wave metrics in conformal gravity, their one point functions, and asymptotic symmetries. One of the metrics is a generalization of the standard pp-waves in Einstein gravity to conformal gravity. The…
We show that in the anisotropic Ho\v{r}ava-Lifshitz gravity there is a well-defined wave zone where the physical degrees of freedom propagate according to a non-relativistic linear evolution equation of high order in spatial derivatives,…
We exhibit blow-up conditions for the gravity water-waves equations in any dimension and in domains with arbitrary bottoms. We follow the method by Alazard, Burq and Zuily of using a paradifferential reduction of the equations and derive…
We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the…
We combine theories of scattering for linearized water waves and flexural waves in thin plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…
We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…