Global Strichartz estimates for approximations of the Schrödinger equation

Article type: Research Article

Authors: Ignat, Liviu I.

Affiliations: Departamento de Matemáticas, Universidad Autónoma de Madrid, Crt. Colmenar Viejo Km. 15, 28049 Madrid, Spain Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania Tel.: +34 914977644, Fax: +34 914974889 E-mail: liviu.ignat@uam.es

Abstract: We consider a semidiscrete scheme for the linear Schrödinger equation with high order dissipative term. We obtain maximum norm estimates for its solutions and we prove global Strichartz estimates for the considered model, estimates that are uniform with respect to the mesh size. The methods we employ are based on classical arguments of harmonic analysis.

Keywords: finite differences, Schrödinger equations, Strichartz estimates

Journal: Asymptotic Analysis, vol. 52, no. 1-2, pp. 37-51, 2007