Related papers: Strichartz estimates for gravity water waves
Here we discuss some issues concerning the statistical properties of ocean surface waves. We show that, using the approach of weak turbulence theory, deviations from Gaussian statistics can be naturally included. In particular we discuss…
Intuitively, crest speeds of water waves are assumed to match their phase velocities. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the…
We consider the two dimensional gravity water waves with nonzero constant vorticity in infinite depth. We show that for $s\geq \frac{3}{4}$, the water waves system is locally well-posed in $\mathcal{H}^{s}$, which is the nonzero constant…
In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $\varepsilon$ in a space of analytic functions which have a…
We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar…
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which…
We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…
In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the wave speed and that the free surface lies everywhere above…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms…
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix…
The purpose of this paper is to show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small…
We prove the Benjamin and Lighthill conjecture for all two-dimensional steady water waves with an arbitrary vorticity distribution. We show that the flow force constant of an arbitrary smooth wave is bounded by the corresponding flow force…
This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…
Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…
We study theoretically the capillary-gravity waves created at the water-air interface by an external surface pressure distribution symmetrical about a point and moving at constant velocity along a linear trajectory. Within the framework of…
We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from \cite{CH2} and arguments borrowed from \cite{HZ, Zhang}.…
In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…