arXiv subjects

David Lafontaine

Publications and source records attributed to David Lafontaine.

21 records · Page 2Linked to original sources

arXiv2018

About the wave equation outside two strictly convex obstacles

We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schrödinger equation. Moreover, we show a first step toward the large data scattering for the critical non linear equation associated to this geometrical setting, and prove the scattering for a class of non trapping obstacles close to the two convex framework.

math.AP↗

arXiv2017

Strichartz estimates without loss outside two strictly convex obstacles

We prove global Strichartz estimates without loss outside two strictly convex obstacles, combining arguments from M.Ikawa (1982,1988) with more recent ones inspired by N.Burq, C.Guillarmou, and A. Hassell (2010) and O. Ivanovici (2010). This is to be contrasted with the loss in the smoothing estimate for the Schrödinger equation with Dirichlet boundary conditions in the presence of a trapped geodesic.

math.AP↗

arXiv2016

Scattering for NLS with a potential on the line

We show the $H^{1}$ scattering for a one dimensional nonlinear Schrödinger equation with a non-negative, repulsive potential $V$ such that $V,xV\in W^{1,1}$, and a mass-supercritical non-linearity. We follow the approach of concentration-compacity/rigidity first introduced by Kenig and Merle.

math.AP↗