Related papers: Finite depth gravity water waves in holomorphic co…
We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow $U(x_2)$, $x_2 \in (-h, 0)$, where the wave numbers $k$ of the horizontal variable $x_1$ is treated as a parameter. Our main…
A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko's equation considered in \cite{KD}. Both operators in the proposed equation are nonlinear and depend on the…
We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…
The gravitational collapse of spherical, barotropic perfect fluids is analyzed here. For the first time, the final state of these systems is studied without resorting to simplifying assumptions - such as self-similarity - using a new…
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 prove the existence of small amplitude time quasi-periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a…
A new type of steady steep two-dimensional irrotational symmetric periodic gravity waves on inviscid incompressible fluid of infinite depth is revealed. We demonstrate that these waves have sharper crests in comparison with the Stokes waves…
The coupling of a stringlike fluid with ordinary matter and gravity may lead to a closed Universe with the dynamic of an open one. This can provide an alternative solution for the age and horizon problems. A study of density perturbations…
We study the tensorial modes of the two-fluid model, where one of this fluids has an equation of state $p = - \rho/3$ (variable cosmological constant, cosmic string fluid, texture) or $p = - \rho$ (cosmological constant), while the other…
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…
We present novel analytical solutions for linear-order gravitational waves or tensor perturbations in a flat Friedmann-Robertson-Walker universe containing two perfect fluids, radiation and pressureless dust, and allowing for neutrino…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…
We compute analytically the tidal field and polarizations of an exact gravitational wave generated by a cylindrical beam of null matter of finite width and length in quadratic curvature gravity. We propose that this wave can represent the…
In this note, we propose several unsolved problems concerning the irrotational oscillation of a water droplet under zero gravity. We will derive the governing equation of this physical model, and convert it to a quasilinear dispersive…
In this paper we consider fundamental processes of the disturbance and propagation of internal gravity waves in the ocean modeled as a vertically stratified, horizontally non-uniform, and non-stationary medium. We develop asymptotic methods…
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…