Related papers: Global regularity for 2d water waves with surface …
In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is…
In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…
This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
We prove that wave maps that factor as $\mathbb{R}^{1+d} \overset{\varphi_{\text{S}}}{\to} \mathbb{R} \overset{\varphi_{\text{I}}}{\to} M$, subject to a sign condition, are globally nonlinear stable under small compactly supported…
The Euler-Korteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasi-linear system that can be recast as a degenerate Schr\"odinger type equation. Local…
We study generic waves without rotational symmetry in (2+1) - dimensional noncommutative scalar field theory. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by…
We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its…
We derive transport equations for the propagation of water wave action in the presence of a static, spatially random surface drift. Using the Wigner distribution $\W(\x,\k,t)$ to represent the envelope of the wave amplitude at position $\x$…
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…
This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential…
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 study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in…
We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is…
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…
A method to find optimal 2nd-order perturbations is presented, and applied to find the optimal spanwise-wavy surface for suppression of cylinder wake instability. Second-order perturbations are required to capture the stabilizing effect of…
In this paper, we investigate the global behaviors of solutions to defocusing semilinear wave equations in $\mathbb{R}^{1+d}$ with $d\geq 3$. We prove that in the energy space the solution verifies the integrated local energy decay…
The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow…
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received intense attention in recent years in the context of…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…