Related papers: Control of water waves
Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension,…
We give an explicit solution describing internal waves with a still water surface, modelling the dead water phenomenon, on the basis of the Gerstner wave solution to the Euler equations.
In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing…
Numerically computed with high accuracy are periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface…
We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradiferential reduction established in the companion paper, we prove Strichartz estimates for solutions to this problem, at a…
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…
In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in $x_1$, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
We consider the two dimensional gravity water wave equation in the regime that includes free surfaces with angled crests. We assume that the fluid is inviscid, incompressible and irrotational, the air density is zero, and we neglect the…
We establish sharp regional observability results for solutions of the wave equation in a bounded domain of $\Omega \subset \mathbb{R}^n$, in case where the geometric control condition is not satisfied. Assuming that the waves are observed…
We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using conformal mappings and a new Babenko-type reformulation of…
This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the…
This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
We consider the motion of the interface separating a vacuum from an inviscid, incompressible, and irrotational fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid motion is…
In this paper, we study solitary waves propagating along the surface of an infinitely deep body of water in two or three dimensions. The waves are acted upon by gravity and capillary effects are allowed --- but not required --- on the…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus $\mathbb{T}=\mathbb{R}/2\pi\mathbb{Z}$. We assume that the control is acting on an open subset…
We prove local well-posedness for the gravity water waves equations without surface tension, with initial velocity field in $H^s$, $s > \frac{d}{2} + 1 - \mu$, where $\mu = \frac{1}{10}$ in the case $d = 1$ and $\mu = \frac{1}{5}$ in the…