Related papers: Exact controllability of the vortex system by mean…
The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…
The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise…
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control.…
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary…
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…
We prove uniqueness for the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti in the case where the vorticity is initially constant near the point vortex. Our method relies on the Eulerian approach for…
Vortices are widely studied in fields ranging from nonlinear optics to magnetic systems and superconductors. A vortex carries a binary information corresponding to its topological charge, `plus' or `minus', that can be used for information…
We study controllability issues for the 2D Euler and Navier-Stokes (NS) systems under periodic boundary conditions. These systems describe motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional torus…
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on 2-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and…
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…
In this paper we consider the problem of controlling pointwise, by means of a time dependent Dirac measure supported by a given point, a coupled system of two Korteweg-de Vries equations on the unit circle. More precisely, by means of…
Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…
Vortices are topological objects representing the circular motion of a fluid. With their additional degree of freedom, the 'vorticity', they have been widely investigated in many physical systems and different materials for fundamental…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of…
We investigate enstrophy variations by collapse of point vortices in an inviscid flow and, in particular, focus on the enstrophy dissipation that is a significant property characterizing 2D turbulent flows. Point vortex is an ideal vortex…
We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove…
This work is focused to study the development and control of the laminar vortex breakdown of a flow enclosed in a cylinder. We show that vortex breakdown can be controlled by the introduction of a small fixed rod in the axis of the…