A version of Hörmander’s theorem for the fractional Brownian motion

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hörmander’s condition. The main new ingredient of the proof is an extension of Norris’ lemma to this situation.     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Weak limits of Palais-Smale sequences for a class of critical functionals

We show that, for two dimensional domains, Palais-Smale sequences for theH-equation functional or the harmonic map functional converge weakly (up to subsequences) to solutions of the equations.     

Skew-product decompositions of Brownian motions on manifolds: A probabilistic aspect of the Lichnerowicz-Szabo theorem

We show that the only compact simply connected manifolds for which the radial part of Brownian motion enjoys the Markov property are compact two points homogeneous spaces, i.e. rank one symmetric spaces.     

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.     

Dispersive estimates and the 2D cubic NLS equation

We prove that the initial value problem for the 2D cubic semi-linear Schrödinger equation is well-posed in the Besov space B _0, ^∞2 (?²). For this, we rely on some new dispersive inequalities derived from bilinear restriction theorems.     

Redox-triggered molecular movement in a multicomponent metal complex in solution and in the solid state

The Cu(I) and Cu(II) complexes of the new 1,8-diferro-cenylmethyl-4,11-dimethyl-1,4,8,11-tetraazacyclotetra-decane ligand (denoted L) have been isolated and characterized by X-ray structure determination and electrochemical studies. The Cu(I) complex presents an unprecedented stability toward dioxygen. The two complexes adopt two energetically distinct and stable geometries, which differ mainly by the relative positioning of the substituents above or below the cyclam plane. Triggered by a copper-centered electron transfer, a fast and reversible motion of the noncoordinating subunits is obtained in homogeneous solution and in the solid state.     

Effect of pressure and temperature upon tin alkoxide-promoted ring-opening polymerisation of epsilon-caprolactone in supercritical carbon dioxide

Ring-opening polymerisation of epsilon-caprolactone in supercritical carbon dioxide is slowed down by a carbonation reaction, resulting in a positive volume of activation and a higher energy of activation as compared to polymerisation in a regular hydrocarbon solvent.     

Scattering on Reissner-Nordstrøm Metric for Massive Charged Spin 1/2 Fields

We consider massive charged Dirac fields on the Reissner-Nordstrøm metric. We prove the existence and asymptotic completeness of wave operators, classical at horizon and modified at infinity. Communicated by Piotr Chrusciel submitted 24/05/02, accepted: 14/02/03