Related papers: Smooth stationary water waves with exponentially l…
We construct small-amplitude solitary traveling gravity-capillary water waves with a finite number of point vortices along a vertical line, on finite depth. This is done using a local bifurcation argument. The properties of the resulting…
We prove variational instability for small-amplitude solutions to the periodic irrotational gravity water wave problem in finite depth. Our results are based on a reformation of the water wave problem as a pseudo-differential Euler-Lagrange…
We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
The study of gravity-capillary water waves in two space dimensions has been an important question in mathematical fluid dynamics. By implementing the cubic modified energy method of Ifrim-Tataru in the context of gravity-capillary waves, we…
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…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
In this paper, we study steady vortex patch solutions to the incompressible Euler equations in a planar bounded domain $D$. Let $\psi_0$ be the solution of the elliptic problem $-\Delta \psi _{0} =1$ in $D$; $\psi_0=0$ on $\partial D$. We…
This paper presents a pioneering investigation into the existence of traveling wave solutions for the two-dimensional Euler equations with constant vorticity in a curved annular domain, where gravity acts radially inward. This configuration…
In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
In this paper we prove rigidity results for classical solutions to the stationary 2D Euler equations in $\mathbb{R}^2$. Assuming that the velocity field has finite energy and that the stagnation set is connected, we prove that the…
In this paper we prove a global regularity result for a quadratic quasilinear model associated to the water waves system with surface tension and no gravity in dimension two (the capillary waves system). The model we consider here retains…
Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions…