Related papers: Shallow water waves generated by a floating object…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show theoretically…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission…
This paper addresses the study of the hierarchical control for the one-dimensional wave equation in intervals with a moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving. When…
The standing surface waves in a rectangular vertically oscillating vessel filled with water (Faraday waves) in the presence of a floating elastic sheet are studied experimentally and theoretically. The threshold amplitude of the instability…
We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the…
In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic…
This paper is devoted to the study of the approximate controllability for a one-dimensional wave equation in domains with moving boundary. This equation models the motion of a string where an endpoint is fixed and the other one is moving.…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed…
Flow control occupies a special place in the fields of partial differential equations (PDEs) and control theory, where the complex behavior of solutions of nonlinear dynamics in very high dimension is not just to be understood but also to…
We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact…
In this article, we investigate certain theoretical aspects of the hierarchical controllability problem in one-dimensional wave equations within a moving domain using Stackelberg strategy. The controls are applied along a portion of the…
We prove the semi-global controllability and stabilization of the $(1+1)$-dimensional wave maps equation with spatial domain $\mathbb{S}^1$ and target $\mathbb{S}^k$. First we show that damping stabilizes the system when the energy is…
We consider the strong stabilization of small amplitude gravity water waves in a two dimensional rectangular domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a…
This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…