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.     

Smoothing and dispersive estimates for 1D Schrödinger equations with BV coefficients and applications

We prove smoothing estimates for Schrödinger equations it_∂?+x_∂(a(x)x_∂?)=0 with a(x)∈BV, real and bounded from below. We then bootstrap these estimates to obtain optimal Strichartz and maximal function estimates, all of which turn out to be identical to the constant coefficient case. We also provide counterexamples showing a∈BV to be in a sense a minimal requirement. Finally, we provide an application to sharp well-posedness for a generalized Benjamin-Ono equation.     

3D Modeling of amplification processes in CPA laser amplifiers

We present here chirped pulse amplification simulations allowing for the extension of the generally used 1D model. The importance of the beam spatial profiles, diffraction and thermal effects in simulations is clearly shown in order to describe with accuracy the gain saturation. Experimental measurements performed on a 100 TW laser validate this calculation. The effects of dispersion and self-focusing are also studied.This revised version was published online in August 2005 with a corrected cover date.     

A profile decomposition approach to the L^\infty _t(L^{3}_x) Navier–Stokes regularity criterion

In this paper we continue to develop an alternative viewpoint on recent studies of Navier–Stokes regularity in critical spaces, a program which was started in the recent work by Kenig and Koch (Ann Inst H Poincaré Anal Non Linéaire 28(2):159–187, 2011). Specifically, we prove that strong solutions which remain bounded in the space ${L^3(\mathbb R ^3)}$ do not become singular in finite time, a known result established by Escauriaza et al. (Uspekhi Mat Nauk 58(2(350)):3–44, 2003) in the context of suitable weak solutions. Here, we use the method of “critical elements” which was recently developed by Kenig and Merle to treat critical dispersive equations. Our main tool is a “profile decomposition” for the Navier–Stokes equations in critical Besov spaces which we develop here. As a byproduct of this tool, assuming a singularity-producing initial datum for Navier–Stokes exists in a critical Lebesgue or Besov space, we show there is one with minimal norm, generalizing a result of Rusin and Sverak (J Funct Anal 260(3):879–891, 2011).     

Blow-up of Critical Besov Norms at a Potential Navier–Stokes Singularity

We prove that if an initial datum to the incompressible Navier–Stokes equations in any critical Besov space \({\dot B^{-1+\frac 3p}_{p,q}({\mathbb {R}}^{3})}\), with \({3 < p, q < \infty}\), gives rise to a strong solution with a singularity at a finite time \({T > 0}\), then the norm of the solution in that Besov space becomes unbounded at time T. This result, which treats all critical Besov spaces where local existence is known, generalizes the result of Escauriaza et al. (Uspekhi Mat Nauk 58(2(350)):3–44, 2003) concerning suitable weak solutions blowing up in \({L^{3}({\mathbb R}^{3})}\). Our proof uses profile decompositions and is based on our previous work (Gallagher et al., Math. Ann. 355(4):1527–1559, 2013), which provided an alternative proof of the \({L^{3}({\mathbb R}^{3})}\) result. For very large values of p, an iterative method, which may be of independent interest, enables us to use some techniques from the \({L^{3}({\mathbb R}^{3})}\) setting.     

Enumeration of lactic acid bacteria: lacuna and improvement areas highlighted by proficiency testing

Accreditation and Quality Assurance - During the 2011 to 2018 food microbiology proficiency testing (PT) schemes organized by REQUASUD, a systematic analytical issue was detected. For the...     

Characterization of a high efficiency, ultrashort pulse shaper incorporating a reflective 4096-element spatial light modulator

We demonstrate pulse shaping via arbitrary phase modulation with a reflective, 1 × 4096 element, liquid crystal spatial light modulator (SLM). The unique construction of this device provides a very high efficiency when the device is used for phase modulation only in a prism based pulse shaper, namely 85%. We also present a single shot characterization of the SLM in the spatial domain and a single shot characterization of the pulse shaper in the spectral domain. These characterization methods provide a detailed picture of how the SLM modifies the spectral phase of an ultrashort pulse.     

High order harmonic generation optimization with an apertured laser beam

We report a systematic study of high order harmonic generation with an infrared laser apertured by an iris, as a function of the aperture size. Measurements were made of harmonic generation efficiency for different gas species, laser energies and focal geometries. Harmonic efficiencies as a function of aperture show a characteristic peaked shape, which is independent of gas species and harmonic order. A one dimensional, time dependent simulation of harmonic generation in a gas cell, taking into account experimentally measured transverse coherence of the laser, closely reproduces the observed behaviours. We show that the aperture diameter which maximizes harmonic yield is the result of a compromise between considerations of focal geometry and ionization (which favour small apertures); and harmonic dipole amplitude and phase (which favour large apertures). Received 31 May 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: kazamias@ensta.fr RID="b" ID="b"UMR 7639 du CNRS