Related papers: Approximate controllability of second grade fluids
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…
This paper is dedicated to approximate controllability for Grushin equation on the rectangle $(x,y) \in (-1,1) \times (0,1)$ with an inverse square potential. This model corresponds to the heat equation for the Laplace-Beltrami operator…
We investigate the two dimensional incompressible Navier-Stokes(NS) and the continuity equations in Cartesian coordinates and Eulerian description for non-Newtonian fluids. As a non-Newtonian viscosity we consider the Ladyzenskaya model…
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity…
In this paper, we consider the Cauchy problem to the basic equations of fluid dynamics on the torus. Firstly, we construct a new initial data and provide a simple proof on the ill-posedness of $B^s_{p,\infty}$ solution of the Euler…
We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets…
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one…
There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of…
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of…
This manuscript is concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order $1<q<2$ in Banach spaces. As far as we know, few articles have investigated this issue. The…
Modern two dimensional conductors with low defect densities and strong electron-electron scattering are favorable platforms for formation of a viscous fluid of conduction electrons. Electric properties of these systems are determined by the…
We study the local controllability properties of 2D and 3D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by Navier-Stokes equations. It is assumed that swimmers'…
We study the 2D Navier-Stokes equations within the framework of a constraint that ensures energy conservation throughout the solution. By employing the Galerkin approximation method, we demonstrate the existence and uniqueness of a global…
We describe a simple classroom demonstration of a fluid-dynamic instability. The demonstration requires only a bucket of water, a piece of string and some used tealeaves or coffee grounds. We argue that the mechanism for the instability, at…
In this article, we prove that the nonlinear Kawahara equation on the periodic domain \(\mathbb{T}\) (the unit circle in the plane) is globally approximately controllable in \(H^s(\mathbb{T})\) for \(s \in \mathbb{N}\), at any time \(T >…
We evaluate the ground state degeneracy of noncommutative Chern-Simons models on the two-torus, a quantity that is interpreted as the "topological order" of associated phases of Hall fluids. We define the noncommutative theory via T-duality…
This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…