Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed in Hainzl (Ann. H. Poincaré, in press). We fix an arbitrary cut-off parameter Λ and recover the α²-term of the self-energy, where α is the coupling parameter representing the fine structure constant. Thereby we develop a method which allows to expand the self-energy up to any power of α. This implies that perturbation theory in α is correct if Λ is fix. As an immediate consequence we obtain enhanced binding for electrons.     

New access to H-phosphonates via metal-catalyzed phosphorus-oxygen bond formation

A novel approach to H-phosphonates from hypophosphorous acid using a transfer hydrogenation process was developed. This method is atom-economical, environmentally friendly, catalytic, and efficient, leading easily to H-phosphonate monoesters or ammonium salt in moderate to good yields.     

THE PHOTOTOXICITY OF 2,5-DIPHENYLOXAZOLE (POP) AND 1,4-BIS(5-PHENYLOXAZOL-2-YL)BENZENE (POPOP)

Abstract 2,5-Diphenyloxazole (POP) is widely used for the determination of radioactivity by scintillation counting. It has been found to be phototoxic to the yeasts Saccharomyces cerevisiae and Candida utilis , to the first instar larvae of the mosquito Aedes aegypti , to the crustaceans Daphnia magna and Artemia salida , as well as to the eggs of Drosophila melanogaster . The related molecule 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP) is also phototoxic, but to a lesser degree. Both POP and POPOP can sensitize the formation of singlet oxygen.     

Expedient synthesis of substituted imidazoles from nitriles

Expedient and practical new methodology for the synthesis of substituted imidazoles was developed to provide a rapid access to a variety of 2-substituted, 1,2-disubstituted and 1,2,4-trisubstituted imidazoles by the direct CuCl-mediated reaction of nitriles with α-amino acetals in an intermolecular as well as intramolecular fashion.