Dispersion estimates for 2D Dirac equation

Article type: Research Article

Authors: Kopylova, E.A.

Affiliations: Faculty of Mathematics, Vienna University, Vienna, Austria | Institute for Information Transmission Problems RAS, Moscow, Russia. E-mail: elena.kopylova@univie.ac.at

Abstract: We obtain a dispersion long-time decay in weighted norms for solutions of the 2D Dirac equation with generic potentials. For high energy component we develop the approach of Boussaid relying on the Mourre estimates and the minimal escape velocity estimates of Hunziker, Sigal and Soffer. For the low energy component we obtain the asymptotics of the resolvent near the thresholds in the nonsingular case and apply 2D version of Jensen–Kato lemma on “one-and-half partial integration”. The results can be applied to the study of asymptotic stability and scattering of solitons for nonlinear 2D Dirac equations.

Keywords: dispersion decay, weighted norms, Dirac equation

DOI: 10.3233/ASY-131166

Journal: Asymptotic Analysis, vol. 84, no. 1-2, pp. 35-46, 2013