Solutions faibles H2 pour un modèle de fluide non newtonien

This Note is devoted to the study a non-linear system modelling a flow of a non-Newtonian fluid, namely aqueous polymer solutions. In the present work, we prove a theorem on the existence of weak solutions for the steady-state problem in a bounded or exterior plane domain. A first difficulty is due to the fact that we search these solutions in the natural space given by the energy inequalities. The second difficulty stems from the fact that the non-linear term involves a third-order derivative, whereas its elliptic term is only a Laplace operator. To cite this article: C. Amrouche, E.-H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Une conduite cylindrique n'est pas optimale pour minimiser l'énergie dissipée par un fluide

We consider an incompressible fluid in a three-dimensional cylindrical pipe, following the Navier–Stokes system with classical boundary conditions on the boundary of the cylinder. We are interested in the following question: is the cylinder the optimal shape for the criterion “energy dissipated by the fluid”? We prove that it is not the case. For that purpose, we explicit the first order optimality condition, thanks to adjoint state and we prove that it is impossible that the adjoint state be a solution of this over-determined system. To cite this article: A. Henrot, Y. Privat, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Evolution d'une singularite ponctuelle dans un fluide compressible

In this work, we study the regularity of the solution of compressible Euler system when the Cauchy data is conormal to this origin. We prove that, outside the origin, the solution is conormal to the disjoint union of a smooth curve and a smooth hypersurface.     

Écoulement d'un fluide de Bingham dans un domaine non-cylindrique

We obtain an existence theorem for Bingham flows in a noncylindrical domain, as a simple application of a previous result on Bingham flows with a monotone perturbation.     

Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

We prove global existence of solutions to the continuous nonhomogeneous Smoluchowski equation for coagulation rates satisfying a more general structure condition than the Galkin–Tupchiev monotony hypothesis considered in (Ph. Laurençot, S. Mischler, Arch. Rational Mech. Anal. 162 (1) (2002) 45–99). The Smoluchowski coagulation rate fulfils this condition as well as some rates which vanish on the diagonal. Under the condition of positivity of the coagulation rate outside of the diagonal we prove that solutions tend to 0 in the large time asymptotic. These results depend on a new estimate from below for the dissipation rate of the L^p-norm, p>1. To cite this article: S. Mischler, M. Rodriguez Ricard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Écoulement d'un fluide de Bingham dans un domaine non-cylindrique avec singularité

We consider a Bingham flow on a noncylindrical domain with a singularity at t = 0. Using the well known technique of Galerkin approximations, we give an existence theorem. For the bidimensional case we also show uniqueness of the solution of our problem.     

Problemes aux limites pour l'equation de boltzmann: existence globale de solutions

This work is concerned by the initial and boundary value problem for the Boltzmann equation. Existence in the large and asymptotic behaviour results are proved for small data and general reemission laws. The colisional kernel satisfies the cut—off angular hypothesesand, the intermolecular potential is such that 7/3 <s≤∞ for the Dirichlet case and 7/3 <s≤5for the general case

Mot—clés: Equation de Boltzmann— Problèmes aux limites intérieurs et extérieurs — Gaz raréfiés —Condition aux limites de Dirichlet— Conditions aux limites non lináeaires— Existence globale de petites solutions     

Existence de deux solutions du type front progressif pour un modèle de combustion avec pertes de chaleur

This Note deals with the existence of planar flames, in the case of a single-step chemical reaction with volumetric heat losses. We prove the existence of two distinct solutions, for small values of the heat loss rate parameter. We also give upper bounds for the flame speed and for the heat loss rate parameter. To cite this article: L. Roques, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Existence et unicité de la solutions faible-renormalisée pour un système non linéaire de Boussinesq

We give existence and uniqueness results of the weak-renormalized solution for a class of nonlinear Boussinesq systems. We establish regularity results for the heat equation which we combine with the usual techniques for Navier–Stokes equations mixed with the tools involved for renormalized solutions. To cite this article: N. Bruyère, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Problème de type Buffon pour un secteur circulaire

Dans ce travail nous étudions un problème de type Buffon pour un réseau de droites du plan euclidienE ₂ dont la cellule fondamentale est un parallélogramme et pour “corps test” un secteur circulaire. AMS Classification: 60D05, 52A22. Travail effectué avec l'aide du MURST (40%, 60%).     

Solutions fondamentales pour un milieu élastique à isotropie transverse

The general solution of an axisymmetric problem for a homogeneous medium is given for a surface concentrated loading, and from it a closed form solution for a point force is deduced. The infinite and semi-infinite spaces are considered for various boundary conditions.     

Mesures quasi-invariantes pour un feuilletage et limites de moyennes longitudinales

In this Note, we generalize a result of Goodman–Plante, who characterizes limit points of averaging sequences as holonomy invariant transverse measures. We prove an analogous result for some leafwise averages, weighted with a cocycle Δ, whose limit points are a product of a quasi-invariant transverse measure with respect to Δ with a leafwise measure. To cite this article: B. Schapira, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Un contre-exemple pour les formes invariantes sur un corps fini

Let A be a Jordan algebra over the reals which is a Banach space with respect to a norm satisfying the requirements: (i) ∥ a ° b ∥ ≤ ∥ a ∥ ∥ b ∥, (ii) ∥ a² ∥ = ∥ a ∥², (iii) ∥ a² ∥ ≤ ∥ a² + b² ∥ for a, b?A. It is shown that A possesses a unique norm closed Jordan ideal J such that $\text{A}\text{J}$ has a faithful representation as a Jordan algebra of self-adjoint operators on a complex Hilbert space, while every “irreducible” representation of A not annihilating J is onto the exceptional Jordan algebra M₃⁸.     

Sul metodo delle approssimazioni successive: Convergenza globale e plus-convergenza globale

With reference to the notions of global convergence and plus-global convergence introduced in [4], we prove that, for a dendriteX with a finite number of end points and a continuous mapF ofX into itself, the successive approximations method relative to pair (X, F) converges globally if and only ifF has no periodic points; furthermore, we show that ifF has no periodic points and the set of fixed points ofF is totally disconnected then the successive approximations method relative to the pair (X, F) plus-converge globally. Some auxiliary propositions have been proved in more general topological areas. One of them refers to a compact metric space (Γ,d′), to a continuous map ? of Γ into itself and to a sequence \((x_n )_{n \in IN} \) of points of Γ such that the sequence \((d^1 (x_{n + 1} ,\varphi (x_n )))_{n \in IN} \) converges to zero, and concerns the set of the cluster points of the sequence \((x_n )_{n \in IN} \) . In the end the global convergence and plus-global convergence in any metric space are characterized.     

Les facteurs de transfert pour les groupes classiques: un formulaire

Within the framework of endoscopy, transfer factors have been defined by Langlands and Shelstad, then by Kottwitz and Shelstad in the twisted case. Using their definition, we give explicit formulas for transfer factors, in the case of classical groups.     

Une preuve courte du principe de Selberg pour un groupe -adique

In 1992, Blanc and Brylinski showed the following property for a -adic group , called the ``abstract Selberg principle': the orbital integrals on conjugacy classes of non-compact elements of the Hattori rank of a finitely generated projective smooth representation of vanish. The proof is by explicit computations of ``low' level ( and cyclic and Hochschild cohomologies. Here we intend to show that this property is actually a direct consequence of two facts: Clozel's integration formula (which leads us to assume the defining characteristic to be zero) and the triviality of the action of unramified characters on the of (which is also proven here, using a standard -theoretic argument due to Grothendieck).

     

Des vortex fractionnaires pour un modèle Ginzburg–Landau spineur

Recent papers in the physics literature have introduced spin-coupled (or spinor) Ginzburg–Landau models for complex vector-valued order parameters in order to account for ferromagnetic or antiferromagnetic effects in high-temperature superconductors and in optically confined Bose–Einstein condensates. In this Note we observe that such models can lead to new types of vortices, with fractional degree and non-trivial core structure. To cite this article: S. Alama, L. Bronsard, C. R. Acad. Sci. Paris, Ser. I 337 (2003).