Sharp Strichartz estimates for some variable coefficient Schrödinger operators on R×T₂

Abstract

In the first part of the paper we continue the study of solutions to Schrödinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schrödinger operator involves a Laplace operator with variable coefficients with a particular dependence on the space variables, then one can prove Strichartz estimates at the same regularity as that needed for constant coefficients. Our work presents a two dimensional analysis, but we expect that with the obvious adjustments similar results are available in higher dimensions.

Keywords

• schrödinger equations on the torus
• variable coefficient schrödinger equations
• strichartz estimates
• periodic nls
• time-degenerate equations