Publications

2015

• Stability in exponential time of Minkowski space-time with a space-like translation symmetry
  
  • Huneau Cécile
  • Huneau Cecile
  , 2014, pp.1 - 14. (10.5802/slsedp.77)
  DOI : 10.5802/slsedp.77
• Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
  
  • Bethuel Fabrice
  • Gravejat Philippe
  • Smets Didier
  Annales Scientifiques de l'École Normale Supérieure, Gauthier-Villars ; Société mathématique de France, 2015, 48 (6), pp.1327-1381. We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the energy space. In particular, our results do not require smallness in some weighted spaces or a priori spectral assumptions. Our strategy is reminiscent of the one used by Martel and Merle in various works regarding generalized Korteweg-de Vries equations. The important feature of our contribution is related to the fact that while Korteweg-de Vries equations possess unidirectional dispersion, Schrödinger equations do not.
• On some extensions of the FKN theorem
  
  • Jendrej Jacek
  • Oleszkiewicz Krzysztof
  • Wojtaszczyk Jakub
  Theory of Computing Systems, Springer Verlag, 2015, 11 (1), pp.445-469. (10.4086/toc.2015.v011a018)
  DOI : 10.4086/toc.2015.v011a018
• The Diffusion Approximation for the Linear Boltzmann Equation with Vanishing Scattering Coefficient
  
  • Bardos Claude
  • Bernard Etienne
  • Golse François
  • Sentis Remi
  Communications in Mathematical Sciences, International Press, 2015, 13 (3), pp.pp. 641-671. The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer in a composite medium with optically thin inclusions in an optically thick background medium. The equation governing the evolution of the approximate particle density coincides with the limit of the diffusion equation with infinite diffusion coefficient in the optically thin inclusions. (10.4310/CMS.2015.v13.n3.a3)
  DOI : 10.4310/CMS.2015.v13.n3.a3