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.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

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).     

Pharmazeutische Pr?parate

Ohne Zusammenfassung     

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.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

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.     

Scattering of Magnetic Edge States

We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering operator attains a limit for large magnetic fields which preserves Landau bands. We interpret the corresponding scattering phases in terms of classical trajectories. Communicated by Yosi Avron submitted 23/02/05, accepted 3/05/05