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Artículo
A new proof of the existence of suitable weak solutions and other remarks for the Navier-Stokes equations
(Scientific Research Publishing, 2018-04)
We prove that the limits of the semi-discrete and the discrete semi-implicit Euler schemes for the 3D Navier-Stokes equations upplemented with Dirichlet boundary conditions are suitable in the sense of Scheffer. This ...
Artículo
Why viscous fluids adhere to rugose walls: A mathematical explanation
(ScienceDirect, 2002-04-29)
The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall covered by microscopic asperities because, due to the viscous dissipation, the surface irregularities ...
Artículo
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
(EDP Sciences, 2006-07)
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂y ∂n + f(y) = 0. We ...
Artículo
Some inverse problems for the Burgers equation and related systems
(Elsevier, 2021-11-23)
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find ...
Artículo
On the control of some coupled systems of the Boussinesq kind with few controls
(AIMS, 2012-06-01)
This paper is devoted to prove the local exact controllability to the trajectories for a coupled system, of the Boussinesq kind, with a reduced number of controls. In the state system, the unknowns are the velocity field ...
Artículo
New results concerning the hierarchical control of linear and semilinear parabolic equations
(E.D.P. Sciences, 2022-02-09)
This paper deals with the application of multiple strategies to control some parabolic PDEs. We assume that we can act on the system through a hierarchy of distributed controls: with a rst control (a follower), we drive ...
Artículo
Insensitizing controls for a large-scale ocean circulation model
(Elsevier, 2003-08-15)
We consider here a linear quasi-geostrophic ocean model. We look for controls insensitizing (resp. ε-insensitizing) an observation function of the state. The existence of such controls is equivalent to a null controllability ...
Artículo
Motivation, analysis and control of the variable density Navier-Stokes equations
(AIMS, 2012-12)
Résultats d’unicité pour des problèmes pseudomonotones avec p > 2. Nous considérons un opérateur pseudomonotone du type −div(b(x, u)|∇ u| p−2∇ u), avec 1 <p< +∞ et b(x, s) une fonction Lipschitzienne en s qui vérifie 0 < ...
Artículo
Sobre la paralelización de problemas elípticos
(Sociedad Española de Matemática Aplicada, 2005-03)
En este trabajo se recogen dos de los problemas que aparecen a la hora de resolver numéricamente las ecuaciones de Navier-Stokes. La discretización en la variabletemporal en dichas ecuaciones nos conduce, en cada etapa ...
Artículo
Controllability of linear and semilinear non-diagonalizable parabolic systems
(EDP Sciences, 2015)
This paper is concerned with the controllability of some (linear and semilinear) nondiagonalizable parabolic systems of PDEs. We will show that the well known null controllability properties of the classical heat equation ...