Existence globale pour le système d'Euler incompressible 2-D dans B∞,11

We prove a global well-posedness result for the two-dimensional Euler system in the critical Besov space $B_{\infty ,1}^1$. We also establish a uniform estimate on the viscosity for the incompressible Navier–Stokes system in that space. An inviscid limit result is also given. To cite this article: T. Hmidi, S. Keraani, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.     

On the global well-posedness for the axisymmetric Euler equations

This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in critical Besov spaces B_p,1^1+3/p{B_{p,1}^{1+3/p}}. In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity.     

Identification of nonlinear Hammerstein system using mixed integer-real coded particle swarm optimization: application to the electric daily peak-load forecasting

This paper investigates the modeling of a class of dynamic systems using nonlinear Hammerstein (NLH) model composed of a memory-less polynomial block cascaded to an autoregressive with exogenous input (ARX) time-series block. The model thus defined is known as NLHARX. Both the integer orders and the real coefficients of the model are identified simultaneously in a unified framework using a new algorithm based on a mixed coded integer-real particle swarm optimization. Unlike classical identification methods which assume the orders to be known in advance, the proposed approach is new since it estimates both the real and integer design parameters while minimizing the error between the outputs of the system and the model. The usefulness and the effectiveness of the proposed approach have been demonstrated through extensive simulations. Two illustrative examples are included in this paper: an empirical example and an application to the forecasting of the daily peak-load of Hail region, Saudi Arabia. Future works will be devoted to the identification of more complex dynamic systems, such as Hammerstein–Wiener and the application to the prediction of time-series related to water and energy.     

The anodic reactivity of 4,4′-dimethoxychalcone: a synthetic and mechanistic investigation

The anodic oxidation of the 4,4′-dimethoxychalcone (DMC) was investigated by different electrochemical methods at a platinum working electrode and in acetonitrile as a solvent. The DMC exhibited a single irreversible anodic peak around 1.6 V versus Ag/AgCl. On the time scale of cyclic voltammetry experiments, the highly reactive radical cation issued from the first electron transfer underwent a second order rate-limiting reaction. The potential imposed electrolyses of DMC led to the formation of a semi-conducting oligomer with 40 % yield. Using different physico-chemicals methods, the structural study confirmed the formation of an o-phenylenevinylene oligomer. The values of the corresponding optical and electrochemical band gaps were calculated to be 3.15 and 2.86 eV, respectively. Finally, a mechanism for the DMC electro-oligomerization was proposed on the basis of the obtained results.     

Global existence and maximal regularity of solutions of gradient systems

In this article, we use a Galerkin method to prove a maximal regularity result for the following abstract gradient system

     

Intermolecular association in liquid N-methylacetamide as studied by x-ray scattering

A structural investigation of liquid N methylacetamide was performed at 308 K using x-ray scattering. To extract the molecular form factor F1(q), the geometry of the conformer which has been found in the crystal is considered. The intermolecular structure function DM(q) is interpreted in terms of H-bonding interactions. The crystal N...O distance is taken into accounted and the number of H bond(s) is assumed to be, respectively, equal to one and two. The liquid structure can be described by a linear dimer or chainlike trimer similar to the ones existing in the crystal. The structure factors SM(q) extracted from these clusters fairly agree with the experimental one beyond q=2.5 A(-1).     

Limite non visqueuse pour le système de Navier–Stokes dans un espace critique

In a recent paper, Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B_2,1². In the present paper we prove that Navier–Stokes system is globally well-posed in B_2,1², with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L² is of order ν. To cite this article: T. Hmidi, S. Keraani, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

On existence of periodic solutions for gradient systems with applications

In this paper we prove the existence of periodic solutions for gradient systems in finite and infinite dimensional spaces. The techniques of the proofs are based on the application of a global inverse functions theorem, the Schäefer fixed point theorem and the Faedou–Galerkin method. We apply our results in order to solve nonlinear reaction–diffusion equations with Dirichlet and Neumann boundary conditions.     

Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces

In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove a global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces Lp, with p∈[1,∞]. Local results for arbitrary initial data are also given.