Related papers: Shallow water waves generated by a floating object…

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…

Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

We obtain a general solution for the water waves resulting from a general, time-dependent surface pressure distribution, in the presence of a shear current of uniform vorticity beneath the surface, in three dimensions. Linearized governing…

We consider the control of a three-dimensional thin liquid film on a flat substrate, inclined at a non-zero angle to the horizontal. Controls are applied via same-fluid blowing and suction through the substrate surface. We consider both…

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a…

We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by a sine wave. The calculation is simple…

We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.

The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to…

Swimming in curved spacetimes is a phenomenon whereby free bodies in curved spacetimes are able to propel themselves by performing cyclic internal motions. When originally proposed, it was further suggested that, in the limit of fast…

We present an analogy between natural oscillations of the standing wave type on a pool of liquid with an interface and a mechanical oscillator model. It is shown that the equations of motion governing both systems have qualitatively similar…

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…

We discuss the linear response to low-frequency tidal forcing of fluid bodies that are slowly and uniformly rotating, are neutrally stratified and may contain a solid or fluid core. This problem may be regarded as a simplified model of…

We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum…

Several meters below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of…

This paper considers the existence and stability properties of two-dimensional solitary waves traversing an infinitely deep body of water. We assume that above the water is vacuum, and that the waves are acted upon by gravity with surface…

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…

An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…

A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently…

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…