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).     

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.     

Viskoelastische Eigenschaften von Polyisobutylenen in verdünnten Lösungen

Zusammenfassung Die Speicher- und VerlustmodulnG undG verdünnter Lösungen (2–4%) dreier Isobutylenpolymerisate mit den Molekulargewichten 0,63, 1,29 und 11×10⁵ wurden in der Apparatur vonBirnboim undFerry über einen Frequenzbereich von 0,4–400 Hz und einen Temperaturbereich von –17,5 bis 25,0° bestimmt. Für die scharf fraktionierten Polymerisate von niederem Molekulargewicht ergab die Frequenzabhängigkeit der Moduln eine ausgezeichnete Übereinstimmung mit der Theorie vonZimm. Die aus den experimentell erhaltenen Kurven ermittelten Molekulargewichte und größten Relaxationszeiten waren von der erwarteten Größenordnung. Für das Polymerisat mit höherem Molekulargewicht entsprach die Frequenzabhängigkeit vonG undG – _s jedoch der Theorie vonRouse. Der Einfluß der hydrodynamischen Wechselwirkung in der Bewegung der Knäuelsegmente, in welchem der Unterschied zwischen den beiden Theorien besteht, erscheint als von der Größe des Molekulargewichts abhängig.

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Summary The storage and loss moduliG andG of dilute (2–4%) solutions of three polyisobutylenes of molecular weight 0.63, 1.29, and 11×10⁵ were determined in the apparatus ofBirnboim andFerry over a frequency range of 0.4 to 400 cps, and a temperature range of –17.0 to 25.0°. The sharply fractionated polymers of low molecular weight showed a frequency dependence in excellent agreement with the theory ofZimm. The experimentally determined molecular weights and terminal relaxation times were of the expected order of magnitude. The frequency dependence of the polymer of highest molecular weight, however, conformed more closely to the theory ofRouse. The influence of the hydrodynamic interaction on the motion of the coil segments, which constitutes the difference in the two theories, appears to depend on the magnitude of the molecular weight.