Elder J. Villamizar-Roa

Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles

Abstract We study the existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized Hukuhara derivative and by using some recent results of fixed point of weakly contractive mappings on partially ordered sets.

The Boussinesq system with mixed nonsmooth boundary data

We treat the stationary Boussinesq system with nonsmooth mixed boundary conditions for the temperature, and nonsmooth Dirichlet boundary condition for the velocity. We prove the existence, the continuous dependence of the solution with respect to the data and the uniqueness of the very weak solution. To cite this article: E.J. Villamizar-Roa et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

On the Nonhomogeneous Navier--Stokes System with Navier Friction Boundary Conditions

We address the issue of existence of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions to the strong solution of the Euler equations with variable density, provided that the initial data converge in

Micropolar Fluids with Vanishing Viscosity

L^{2}

On the existence of infinite energy solutions for nonlinear Schrödinger equations

to a smooth enough limit.

A Boundary Control Problem for Micropolar Fluids

A study of the convergence of weak solutions of the nonstationary micropolar fluids, in bounded domains of ℝ𝑛, when the viscosities tend to zero, is established. In the limit, a fluid governed by an Euler-like system is found.

On the Rayleigh–Bénard–Marangoni system and a related optimal control problem

r. We derive new results about existence and uniqueness of local and global solutions for the nonlinear Schrodinger equation, including self-similar solutions. Our analysis is performed in the framework of weak-L P spaces.

On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations

An optimal boundary control problem for the micropolar fluid equations in 3D bounded domains, with mixed boundary conditions, is analyzed. By considering boundary controls for the velocity vector and the angular velocity of rotation of particles, the existence of optimal solutions is proved. The analyzed optimal boundary control problem includes the minimization of a Lebesgue norm between the velocities and some desired fields, as well as the resistance in the fluid due to the viscous friction. By using the Theorem of Lagrange multipliers, an optimality system is derived. A second-order sufficient condition is also given.

Interval-valued functions in a quotient space

Abstract In this paper, we study a boundary control problem associated to the stationary Rayleigh–Benard–Marangoni (RBM) system in presence of controls for the velocity and the temperature on parts of the boundary. We analyze the existence, uniqueness and regularity of weak solutions for the stationary RBM system in polyhedral domains of R 3 , and then, we prove the existence of the optimal solution. By using the Theorem of Lagrange multipliers, we derive an optimality system. We also give a second-order sufficient optimality condition and we establish a result of uniqueness of the optimal solution.

Partial Differential EquationsThe Boussinesq system with mixed nonsmooth boundary dataLe système de Boussinesq à données limites mixtes peu regulières

This paper is devoted to the Boussinesq equations that models natural convection in a viscous fluid by coupling Navier-Stokes and heat equations via a zero order approximation. We consider the problem in \begin{document}