Related papers: On the existence of steady periodic capillary-grav…
Analytic methods show stability of the stationary accretion of test fluids but they are inconclusive in the case of self-gravitating stationary flows. We investigate numerically stability of those stationary flows onto compact objects that…
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size $\epsilon$, is almost…
We prove local exact controllability in arbitrary short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrary small amplitude periodic…
We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
We develop a time-dependent conformal method to study the effect of viscosity on steep surface waves. When the effect of surface tension is included, numerical solutions are found that contain highly oscillatory parasitic capillary ripples.…
Using standard signal processing tools, we experimentally report that intermittency of wave turbulence on the surface of a fluid occurs even when two typical large-scale coherent structures (gravity wave breakings and bursts of capillary…
The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis…
We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.
We prove the existence of nonradial classical solutions to the 2D incompressible Euler equations with compact support. More precisely, for any positive integer $k$, we construct compactly supported stationary Euler flows of class…
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude…
We investigate the formal stability of finite-amplitude non-zonal flows bifurcating from the trivial state in the unforced 2D Euler equations on the sphere. To bypass the degeneracy of the spherical Laplacian and filter out the…
This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric…
Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…
In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…