相关论文: Steady periodic water waves bifurcating for fixed-…

This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or…

A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large scale flows (mean…

For two-dimensional steady pure-gravity water waves with a unidirectional flow of constant favourable vorticity, we prove an explicit bound on the amplitude of the wave, which decays to zero as the vorticity tends to infinity. Notably, our…

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…

In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and…

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

This paper investigates the existence of periodic solutions in blood flow propagating through vessels with free boundary conditions via the bifurcation theory. It is rigorously proved that a local $C^1$-curve of small-amplitude periodic…

In this paper we construct periodic capillarity-gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by reexpressing, in the height function formulation of the water wave problem, the boundary condition…

We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…

We investigate within the framework of linear theory the behaviour of the total (hydrodynamic) pressure and of the dynamic pressure in a regular wave train which propagates at the surface of water with a flat bed in a flow with constant…

This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical…

In this paper, we investigate the modulational stability of periodic traveling waves in a local model for shallow water waves, which is an extended version of the Hunter-Saxton equation. We construct a family of small-amplitude periodic…

We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…

We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…

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 a recent paper, Hur & Wheeler [J. Differential Equations, 338:572-590, 2022] proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow under the influence of gravity. These…

For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families…

We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…

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 present a new kind of particle path in constant vorticity water of finite depth, within the framework of small-amplitude waves.