Related papers: Controllability of the 3D compressible Euler syste…

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary…

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…

There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for…

The theory of controlled mechanical systems of [6, 3, 4] is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and…

This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline…

A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by…

In this work, we introduce and study the controllability of the trajectories of a linear dynamical system, which can be used to solve the minimization of a quadratic function in finite dimension. We named this dynamical system the…

The well-posedness of Cauchy problem of 3D compressible Euler equations is studied. By using Smith-Tataru's approach \cite{ST}, we prove the local existence, uniqueness and stability of solutions for Cauchy problem of 3D compressible Euler…

In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…

This paper focuses on the study of the density-dependent incompressible Euler equations in space dimension $d=2$, for low regularity (\textsl{i.e.} non-Lipschitz) initial data satisfying assumptions in spirit of the celebrated Yudovich…

We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a…

In this work we study one problem of mathematical interest for their applications in several topics in Applied Science. We study simultaneous controllability of a pair of systems which model the evolution of sound in a compressible ow…

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…

This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state…

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the…

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…

We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large,…

We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical…